Pub Date : 2019-05-23DOI: 10.11648/J.SJAMS.20190701.11
Muthuri Evans Kithure, A. Waititu, A. Wanjoya
Taxation is one of the means by which governments finance their expenditure by imposing charges on citizens and corporate entities. Kenya Revenue Authority (KRA) is the agency responsible for the assessment, collection and accounting for of all revenues that are due to government. Volatile government revenue is a challenge for fiscal policy makers since it creates risks to government service provision and can make planning difficult, as revenue falls short of expenditure needs both frequently and unexpectedly. The main objective of this study was to model and forecast the volatility of VAT revenue collected in Kenya as well as computing its value at risk and the expected shortfall. Secondary data on daily VAT revenue collections for a period of 3 years was analyzed. The first step was to model the mean equation of the return series using the ARIMA model and ARIMA(3,0,3) was identified to be the most suitable since it had the least values of AIC and BIC. The Lagrange Multiplier test confirmed the presence of ARCH effects using the residuals of the mean equation. A number of heteroscedastic models were fitted and the TGARCH family (ARIMA(3,0,3)/TGARCH(1,2)) was preferred to fit the volatility of the returns. One step ahead forecasting of volatility of the returns was done using the model which gave a value of 7.212. Estimation of value at risk and expected shortfall involved use of POT method by fitting a GPD function to the return data series. The first step was determination of threshold by use of MRL plot and later fitting a GPD function to the return data series using the threshold. The shape, location and scale parameters were estimated using MLE and they were later used to compute the VaR loss and ES at 95% and 99% confidence intervals. The VaR at 95% and 99% was 1.45% and 1.49% respectively while the ES at both the intervals was 0.04% and 0.1% respectively. This study concluded that volatility is persistent in the daily VAT revenue collections and it can easily be modelled using conditional heteroscedastic models.
{"title":"Modelling and Forecasting Volatility of Value Added Tax Revenue in Kenya","authors":"Muthuri Evans Kithure, A. Waititu, A. Wanjoya","doi":"10.11648/J.SJAMS.20190701.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20190701.11","url":null,"abstract":"Taxation is one of the means by which governments finance their expenditure by imposing charges on citizens and corporate entities. Kenya Revenue Authority (KRA) is the agency responsible for the assessment, collection and accounting for of all revenues that are due to government. Volatile government revenue is a challenge for fiscal policy makers since it creates risks to government service provision and can make planning difficult, as revenue falls short of expenditure needs both frequently and unexpectedly. The main objective of this study was to model and forecast the volatility of VAT revenue collected in Kenya as well as computing its value at risk and the expected shortfall. Secondary data on daily VAT revenue collections for a period of 3 years was analyzed. The first step was to model the mean equation of the return series using the ARIMA model and ARIMA(3,0,3) was identified to be the most suitable since it had the least values of AIC and BIC. The Lagrange Multiplier test confirmed the presence of ARCH effects using the residuals of the mean equation. A number of heteroscedastic models were fitted and the TGARCH family (ARIMA(3,0,3)/TGARCH(1,2)) was preferred to fit the volatility of the returns. One step ahead forecasting of volatility of the returns was done using the model which gave a value of 7.212. Estimation of value at risk and expected shortfall involved use of POT method by fitting a GPD function to the return data series. The first step was determination of threshold by use of MRL plot and later fitting a GPD function to the return data series using the threshold. The shape, location and scale parameters were estimated using MLE and they were later used to compute the VaR loss and ES at 95% and 99% confidence intervals. The VaR at 95% and 99% was 1.45% and 1.49% respectively while the ES at both the intervals was 0.04% and 0.1% respectively. This study concluded that volatility is persistent in the daily VAT revenue collections and it can easily be modelled using conditional heteroscedastic models.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"281 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122946031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-16DOI: 10.11648/j.sjams.20180606.11
Mahmoud Ragab
Sorting data is one of the most important problems that play an important rule in many applications in operations research, computer science and many other applications. Many sorting algorithms are well studied but the problem is not to find a way or algorithm to sort elements, but to find an efficiently way to sort elements and do the job. The output is a stream of data in time and it is a sorted data array. We are interested in this flow of data to estaplish a smart technique to sort elements as well as efficient complexity. For the performance of such algorithms, there has been little research on their stochastic behavior and mathematical properties such existance and convergence properties. In this paper we study the mathematical behavior of some different versions sorting algorithms in the case when the size of the input is very large. This work also discuss the corresponding running time using some different strategies in terms of number of comparisons and swaps. Here, we use a nice approach to show the existence of partial sorting process via the weighted branching process. This approach was inspired by the methods used for the analysis of Quickselect and Quichsort in the standard cases, where fixed point equations on the Cadlag space were considered for the first time.
{"title":"Performance Analysis of Sorting Process with Different Sampling Strategies","authors":"Mahmoud Ragab","doi":"10.11648/j.sjams.20180606.11","DOIUrl":"https://doi.org/10.11648/j.sjams.20180606.11","url":null,"abstract":"Sorting data is one of the most important problems that play an important rule in many applications in operations research, computer science and many other applications. Many sorting algorithms are well studied but the problem is not to find a way or algorithm to sort elements, but to find an efficiently way to sort elements and do the job. The output is a stream of data in time and it is a sorted data array. We are interested in this flow of data to estaplish a smart technique to sort elements as well as efficient complexity. For the performance of such algorithms, there has been little research on their stochastic behavior and mathematical properties such existance and convergence properties. In this paper we study the mathematical behavior of some different versions sorting algorithms in the case when the size of the input is very large. This work also discuss the corresponding running time using some different strategies in terms of number of comparisons and swaps. Here, we use a nice approach to show the existence of partial sorting process via the weighted branching process. This approach was inspired by the methods used for the analysis of Quickselect and Quichsort in the standard cases, where fixed point equations on the Cadlag space were considered for the first time.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127392326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-12DOI: 10.11648/j.sjams.20180604.14
Tesfahun Zewde Legisso, Markos Abiso Erango
HIV/AIDS is a major development concern in many countries and is destroying the lives and livelihoods of many people around the world. This study is aimed to assess the demographic and HIV related risk behavior factors that may affect HIV status of the visitors of VCT centers. A cross sectional study was conducted in Gamo-Gofa districts, Southern Nations Nationalities and Peoples Regional State of Ethiopia. A total of 4028 sample were selected using stratified random sampling technique. Data were collected with a designed questionnaire from 20 voluntary counseling and testing center of the districts. If the clients visit VCT center is HIV-infected, it is categorized as HIV positive and if the client test is indicated not HIV-infected, then the visitor categorized as HIV negative status. The Binary logistic regression model was used to analyze the data using the SPSS software. The results of the study revealed that the probability of an individual being HIV positive was 0.0286 and the predictor’s variables age, marriage status, education level, alcohol use, knowledge about HIV, monthly income, condom use and residence of the individual were significantly effect on being HIV-positive. Health professionals and responsible bodies should work on these significant variables to reduce the probability of being HIV positive.
{"title":"The Effect of HIV Related Risk Factors on HIV Status: A Case of Gamo-Gofa Free Standing Voluntary Counseling and Testing Center","authors":"Tesfahun Zewde Legisso, Markos Abiso Erango","doi":"10.11648/j.sjams.20180604.14","DOIUrl":"https://doi.org/10.11648/j.sjams.20180604.14","url":null,"abstract":"HIV/AIDS is a major development concern in many countries and is destroying the lives and livelihoods of many people around the world. This study is aimed to assess the demographic and HIV related risk behavior factors that may affect HIV status of the visitors of VCT centers. A cross sectional study was conducted in Gamo-Gofa districts, Southern Nations Nationalities and Peoples Regional State of Ethiopia. A total of 4028 sample were selected using stratified random sampling technique. Data were collected with a designed questionnaire from 20 voluntary counseling and testing center of the districts. If the clients visit VCT center is HIV-infected, it is categorized as HIV positive and if the client test is indicated not HIV-infected, then the visitor categorized as HIV negative status. The Binary logistic regression model was used to analyze the data using the SPSS software. The results of the study revealed that the probability of an individual being HIV positive was 0.0286 and the predictor’s variables age, marriage status, education level, alcohol use, knowledge about HIV, monthly income, condom use and residence of the individual were significantly effect on being HIV-positive. Health professionals and responsible bodies should work on these significant variables to reduce the probability of being HIV positive.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117128356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, water shortage is increasingly severe, which has huge negative influence on daily life. Constructing hydropower engineering is one of the approaches to alleviate such problem. Therefore, it’s worth settling technical problems of hydropower engineering timely, which will help people not only make better use of water resources but also get rid of various security risks. To achieve such goal, this study predicts potential technical problems that hydropower engineering might happen. In order to utilize the large amount of data, data mining techniques are used to solve this multi-classification problem. First of all, plenty of data is preprocessed. Particularly, because of the complexity of text data, text mining techniques are applied to transform the unstructured data to structural data. Then, eXtreme Gradient Boosting (XGBoost) is applied to make the classification. To validate efficiency of the model, comparisons are made among XGBoost, Gradient Boosting Decision Tree, Random Forest, Decision Tree, k-Nearest Neighbor and Bernoulli Naive Bayes from the perspective of accuracy, precision, recall and f-score. The experimental result shows that XGBoost is more suitable to solve this classification problem. This study provides engineering inspectors with helpful suggestions of particular technical problems that need attention, and further enables people to inspect engineering more efficiently and effectively.
{"title":"Predicting Technical Problems of Hydropower Engineering Using eXtreme Gradient Boosting","authors":"Jing Zhu, Yi Chen, Limin Huang, Chunyong She, Yangfeng Wu, Wenyu Zhang","doi":"10.11648/J.SJAMS.20180604.13","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20180604.13","url":null,"abstract":"Nowadays, water shortage is increasingly severe, which has huge negative influence on daily life. Constructing hydropower engineering is one of the approaches to alleviate such problem. Therefore, it’s worth settling technical problems of hydropower engineering timely, which will help people not only make better use of water resources but also get rid of various security risks. To achieve such goal, this study predicts potential technical problems that hydropower engineering might happen. In order to utilize the large amount of data, data mining techniques are used to solve this multi-classification problem. First of all, plenty of data is preprocessed. Particularly, because of the complexity of text data, text mining techniques are applied to transform the unstructured data to structural data. Then, eXtreme Gradient Boosting (XGBoost) is applied to make the classification. To validate efficiency of the model, comparisons are made among XGBoost, Gradient Boosting Decision Tree, Random Forest, Decision Tree, k-Nearest Neighbor and Bernoulli Naive Bayes from the perspective of accuracy, precision, recall and f-score. The experimental result shows that XGBoost is more suitable to solve this classification problem. This study provides engineering inspectors with helpful suggestions of particular technical problems that need attention, and further enables people to inspect engineering more efficiently and effectively.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134120373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-21DOI: 10.11648/j.sjams.20180604.12
C. Subaar, Juliana Awune Asechoma, Vincent Ninmaal Asigri, Victor Alebna, Francis Xavier Adams
This is an interventional study sought to find the difference in the performance of pupils who were taught using sets of objects (sets model) and paper folding activities, to solve word problems involving addition and subtraction of proper fractions. A total of thirty pupils, of Navrongo Presbyterian Primary School Basic Five A, were used in the study. A well-structured lesson, with teaching and learning materials, was used. A pretest and posttest assessments were deployed to ascertain the effect of the interventional teaching strategies. Prior, to the intervention of the study, 73.3% of the pupils (total of 30) scored below the average mark ranging from 5-7. These represented the experimental group of the study. 26.7% of the pupils (control group) scored the average mark. However, after the intervention, both strategies (sets of objects and paper folding activities) showed remarkable performance. Although both strategies showed remarkable performance in pupils, 59% of the experimental group (total of 22 pupils) scored above the average mark in the paper folding as compared to 50% of the experimental group who scored above the average mark in the usage of sets model. While 87.5% of the control group scored above the average marks ranging from 8-10 during the paper folding activities, 62.5% of the control group scored above the average marks from 8-10 during the use of sets model. The posttest results of both the control and experimental groups taught using paper folding performed far better compared to sets model. The study has shown that pupils’ level of performance had improved drastically with the help of paper folding method. In conclusion, paper folding activities help pupils to appreciate word problems involving addition and subtraction of proper fractions.
{"title":"Towards the Solution of Abysmal Performance of Fraction in Navrongo Presbyterian Primary School: Comparing the Sets of Objects and Paper Folding Designed Interventions","authors":"C. Subaar, Juliana Awune Asechoma, Vincent Ninmaal Asigri, Victor Alebna, Francis Xavier Adams","doi":"10.11648/j.sjams.20180604.12","DOIUrl":"https://doi.org/10.11648/j.sjams.20180604.12","url":null,"abstract":"This is an interventional study sought to find the difference in the performance of pupils who were taught using sets of objects (sets model) and paper folding activities, to solve word problems involving addition and subtraction of proper fractions. A total of thirty pupils, of Navrongo Presbyterian Primary School Basic Five A, were used in the study. A well-structured lesson, with teaching and learning materials, was used. A pretest and posttest assessments were deployed to ascertain the effect of the interventional teaching strategies. Prior, to the intervention of the study, 73.3% of the pupils (total of 30) scored below the average mark ranging from 5-7. These represented the experimental group of the study. 26.7% of the pupils (control group) scored the average mark. However, after the intervention, both strategies (sets of objects and paper folding activities) showed remarkable performance. Although both strategies showed remarkable performance in pupils, 59% of the experimental group (total of 22 pupils) scored above the average mark in the paper folding as compared to 50% of the experimental group who scored above the average mark in the usage of sets model. While 87.5% of the control group scored above the average marks ranging from 8-10 during the paper folding activities, 62.5% of the control group scored above the average marks from 8-10 during the use of sets model. The posttest results of both the control and experimental groups taught using paper folding performed far better compared to sets model. The study has shown that pupils’ level of performance had improved drastically with the help of paper folding method. In conclusion, paper folding activities help pupils to appreciate word problems involving addition and subtraction of proper fractions.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114263287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-11DOI: 10.11648/J.SJAMS.20180604.11
Sarah A. Stanley, J. Tubbs
Background : Several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. In this article, we present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. The existing methods utilize GLMs for binary data when the expected value equals the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Objective : The new method directly models the placement values through beta regression. Methods : We compare the proposed method to the existing models with simulation and a clinical study. Conclusion : The proposed method performs favorably with the commonly used parametric method and has better performance than the semi-parametric method when modeling the covariate adjusted ROC regression.
{"title":"Beta Regression for Modeling a Covariate Adjusted ROC","authors":"Sarah A. Stanley, J. Tubbs","doi":"10.11648/J.SJAMS.20180604.11","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20180604.11","url":null,"abstract":"Background : Several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. In this article, we present an alternative to two existing parametric and semi-parametric methods for estimating a covariate adjusted ROC. The existing methods utilize GLMs for binary data when the expected value equals the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Objective : The new method directly models the placement values through beta regression. Methods : We compare the proposed method to the existing models with simulation and a clinical study. Conclusion : The proposed method performs favorably with the commonly used parametric method and has better performance than the semi-parametric method when modeling the covariate adjusted ROC regression.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"1980 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120847203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-06DOI: 10.11648/J.SJAMS.20180603.15
Edward Akurugu, Abdul-Majeed Issahaku, Abdul-Samed Aliou
The issue of waste management has become a daunting challenge for many countries particularly for developing countries. The adverse effects of waste on human lives and the environment have reached scary levels that call for a thorough assessment of waste management systems across the globe and in particular developing countries. In Bolgatanga municipality of the Upper East Region of Ghana, the situation of waste disposal is appalling exposing residents to all kinds of health related risk. City authorities who have the responsibility of ensuring that the environment is clean and safe for habitation are confronted with the serious burden of managing waste disposal in the municipality. This study therefore sought to examine a set of 18 variables relevant to the topic under investigation and how they relate to influence solid waste management in the municipality from the perspective of residents of the Bolgatanga municipality through the application of Factor Analysis. The object of this approach is to identify a set of indicator variables that amalgamate to form common factors. The opinions of 400 subjects on Solid Waste Management in the municipality were successfully collected through the administration of questionnaires and analyzed. A preliminary analysis of the data showed that the correlation matrix was not an identity matrix and a KMO value of 0.797 described as “middling” was obtained. These provided the necessary and sufficient grounds for the application of Factor Analysis to the data. Further analysis of the data revealed five latent factors which are Institutional Dormancy, Financial Constraint, Infrastructural Lapses, Accessibility and Behavioral Canker as factors that need to be addressed in order to improve the status of Solid Waste Management in Bolgatanga municipality.
{"title":"Application of Factor Analysis in the Assessment of Solid Waste Management in Bolgatanga Municipality of Ghana","authors":"Edward Akurugu, Abdul-Majeed Issahaku, Abdul-Samed Aliou","doi":"10.11648/J.SJAMS.20180603.15","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20180603.15","url":null,"abstract":"The issue of waste management has become a daunting challenge for many countries particularly for developing countries. The adverse effects of waste on human lives and the environment have reached scary levels that call for a thorough assessment of waste management systems across the globe and in particular developing countries. In Bolgatanga municipality of the Upper East Region of Ghana, the situation of waste disposal is appalling exposing residents to all kinds of health related risk. City authorities who have the responsibility of ensuring that the environment is clean and safe for habitation are confronted with the serious burden of managing waste disposal in the municipality. This study therefore sought to examine a set of 18 variables relevant to the topic under investigation and how they relate to influence solid waste management in the municipality from the perspective of residents of the Bolgatanga municipality through the application of Factor Analysis. The object of this approach is to identify a set of indicator variables that amalgamate to form common factors. The opinions of 400 subjects on Solid Waste Management in the municipality were successfully collected through the administration of questionnaires and analyzed. A preliminary analysis of the data showed that the correlation matrix was not an identity matrix and a KMO value of 0.797 described as “middling” was obtained. These provided the necessary and sufficient grounds for the application of Factor Analysis to the data. Further analysis of the data revealed five latent factors which are Institutional Dormancy, Financial Constraint, Infrastructural Lapses, Accessibility and Behavioral Canker as factors that need to be addressed in order to improve the status of Solid Waste Management in Bolgatanga municipality.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124525867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-23DOI: 10.11648/J.SJAMS.20180603.14
Millicent Kithinji, Lucy Muthoni
Public debt is a key economic variable. It is the totality of public and publicly guaranteed debt owed by any level of government to either citizens or foreigners or both. Due to recent debt crises in countries such as Portugal, Italy, Ireland, Greece and Spain, debt control has become a key important fiscal policy of every government. In this study, we applied a Public debt ceiling explicit formula to find out the optimal public debt ceiling for Kenya [3]. We made modification to subjective variables in the explicit formula and used the formula to find the optimal public debt ceiling for Kenya. We illustrate that it is prudent for that government to use a fiscal policy that maintains the debt ratio under an optimal debt ceiling.
{"title":"Determination of optimal public debt ceiling for Kenya using stochastic control","authors":"Millicent Kithinji, Lucy Muthoni","doi":"10.11648/J.SJAMS.20180603.14","DOIUrl":"https://doi.org/10.11648/J.SJAMS.20180603.14","url":null,"abstract":"Public debt is a key economic variable. It is the totality of public and publicly guaranteed debt owed by any level of government to either citizens or foreigners or both. Due to recent debt crises in countries such as Portugal, Italy, Ireland, Greece and Spain, debt control has become a key important fiscal policy of every government. In this study, we applied a Public debt ceiling explicit formula to find out the optimal public debt ceiling for Kenya [3]. We made modification to subjective variables in the explicit formula and used the formula to find the optimal public debt ceiling for Kenya. We illustrate that it is prudent for that government to use a fiscal policy that maintains the debt ratio under an optimal debt ceiling.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130468863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-19DOI: 10.11648/j.sjams.20180603.13
Xingyu Chen, Dirong Chen
In recent decades, functional data have become a commonly encountered type of data. Its ideal units of observation are functions defined on some continuous domain and the observed data are sampled on a discrete grid. An important problem in functional data analysis is how to fit regression models with scalar responses and functional predictors (scalar-on-function regression). This paper focuses on the nonparametric approaches to this problem. First there is a review of the classical k-nearest neighbors (kNN) method for functional regression. Then the mutual nearest neighbors (MNN) method, which is a variant of kNN method, is applied to functional regression. Compared with the classical kNN approach, the MNN method takes use of the concept of mutual nearest neighbors to construct regression model and the pseudo nearest neighbors will not be taken into account during the prediction process. In addition, any nonparametric method in the functional data cases is affected by the curse of infinite dimensionality. To prevent this curse, it is legitimate to measure the proximity between two curves via a semi-metric. The effectiveness of MNN method is illustrated by comparing the predictive power of MNN method with kNN method first on the simulated datasets and then on a real chemometrical example. The comparative experimental analyses show that MNN method preserves the main merits inherent in kNN method and achieves better performances with proper proximity measures.
{"title":"The Mutual Nearest Neighbor Method in Functional Nonparametric Regression","authors":"Xingyu Chen, Dirong Chen","doi":"10.11648/j.sjams.20180603.13","DOIUrl":"https://doi.org/10.11648/j.sjams.20180603.13","url":null,"abstract":"In recent decades, functional data have become a commonly encountered type of data. Its ideal units of observation are functions defined on some continuous domain and the observed data are sampled on a discrete grid. An important problem in functional data analysis is how to fit regression models with scalar responses and functional predictors (scalar-on-function regression). This paper focuses on the nonparametric approaches to this problem. First there is a review of the classical k-nearest neighbors (kNN) method for functional regression. Then the mutual nearest neighbors (MNN) method, which is a variant of kNN method, is applied to functional regression. Compared with the classical kNN approach, the MNN method takes use of the concept of mutual nearest neighbors to construct regression model and the pseudo nearest neighbors will not be taken into account during the prediction process. In addition, any nonparametric method in the functional data cases is affected by the curse of infinite dimensionality. To prevent this curse, it is legitimate to measure the proximity between two curves via a semi-metric. The effectiveness of MNN method is illustrated by comparing the predictive power of MNN method with kNN method first on the simulated datasets and then on a real chemometrical example. The comparative experimental analyses show that MNN method preserves the main merits inherent in kNN method and achieves better performances with proper proximity measures.","PeriodicalId":422938,"journal":{"name":"Science Journal of Applied Mathematics and Statistics","volume":"299 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128618421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-07DOI: 10.11648/J.SJAMS.20180603.12
D. Zhou, Weihua Guo, Hengzhen Huang
Computer simulations have been receiving a lot of attention in industrial engineering as the rapid growth in computer power and numerical techniques. In contrast to physical experiments which are usually carried out in factories, laboratories or fields, computer simulations can save considerable time and cost. From the statistical perspective, the current research work about computer simulations is mostly focusing on modeling the relationship between the output variable from the simulator and the input variables set by the experimenter. However, an experimental design with careful selection of the values of the input variables can significantly affect the quality of the statistical model. Specifically, prediction on the edge area of the experimental domain, which is extremely critical for an industrial engineering experiment often suffers from inadequate data information because the design points usually do not well cover the edge area of the experimental domain. To address this issue, a new type of design, called semi-LHD is proposed in this paper. Such a design type has the following appealing properties: (1) it encompasses a Latin hypercube design as a sub-design so that the design points are uniformly scattered over the interior of the design region; and (2) it possesses some extra marginal design points which are close to the edge so that the prediction accuracy on the edge area of the experimental domain is fully taken into account. Detailed algorithms for finding the marginal design points and how to construct the proposed semi-LHDs are given. Numerical comparisons between the proposed semi-LHDs with the commonly-used Latin hypercube designs, in terms of prediction accuracy, are illustrated through simulation studies. It turns out that the proposed semi-LHDs yield desirable prediction accuracy not only in the interior but also on the edge area of the experimental domain, so they are recommended as the experimental designs for simulation-based industrial engineering experiments.
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