Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1622190
H. Artigue, Gary Smith
Abstract Principal components regression (PCR) reduces a large number of explanatory variables in a regression model down to a small number of principal components. PCR is thought to be more useful, the more numerous the potential explanatory variables. The reality is that a large number of candidate explanatory variables does not make PCR more valuable; instead, it magnifies the failings of PCR.
{"title":"The principal problem with principal components regression","authors":"H. Artigue, Gary Smith","doi":"10.1080/25742558.2019.1622190","DOIUrl":"https://doi.org/10.1080/25742558.2019.1622190","url":null,"abstract":"Abstract Principal components regression (PCR) reduces a large number of explanatory variables in a regression model down to a small number of principal components. PCR is thought to be more useful, the more numerous the potential explanatory variables. The reality is that a large number of candidate explanatory variables does not make PCR more valuable; instead, it magnifies the failings of PCR.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1622190","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47499539","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 : 2019-01-01DOI: 10.1080/25742558.2019.1643438
B. N. Tiwari, A. A. Chathurika
Abstract In this paper, we examine the optimization of Richardson numerical integration of an arbitrary real valued function in the space of step sizes. Namely, as one of the most efficient numerical integrations of an integrable function, the Richardson method is optimized under the variations of its step sizes. Subsequently, we classify the stability domains of the Richardson integration of real valued functions. We discuss stability criteria of the Richardson integration via the sign of the fluctuation discriminant as a quintic or lower degree polynomials as a function of the step size parameter. As special cases, our proposal optimizes the trapezoidal, Romberg and other numerical integrations. Hereby, we consider the optimization of the Richardson schemes as a weighted estimation in the light of extrapolation techniques. Finally, optimal Richardson integrations are discussed towards prospective theoretical and experimental applications and their industrial counterparts.
{"title":"Optimization of the richardson integration over fluctuations of its step sizes","authors":"B. N. Tiwari, A. A. Chathurika","doi":"10.1080/25742558.2019.1643438","DOIUrl":"https://doi.org/10.1080/25742558.2019.1643438","url":null,"abstract":"Abstract In this paper, we examine the optimization of Richardson numerical integration of an arbitrary real valued function in the space of step sizes. Namely, as one of the most efficient numerical integrations of an integrable function, the Richardson method is optimized under the variations of its step sizes. Subsequently, we classify the stability domains of the Richardson integration of real valued functions. We discuss stability criteria of the Richardson integration via the sign of the fluctuation discriminant as a quintic or lower degree polynomials as a function of the step size parameter. As special cases, our proposal optimizes the trapezoidal, Romberg and other numerical integrations. Hereby, we consider the optimization of the Richardson schemes as a weighted estimation in the light of extrapolation techniques. Finally, optimal Richardson integrations are discussed towards prospective theoretical and experimental applications and their industrial counterparts.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1643438","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44325650","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 : 2019-01-01DOI: 10.1080/25742558.2019.1649788
M. Koçak, Jiajing Wang, R. Krukowski, W. Talcott, R. Klesges
Abstract The Health Utilities Index (HUI) questionnaire provides a mechanism to assess intervention effectiveness in multi-attribute health-related quality of life utilizing a set of health status classification systems. It is a comprehensive and valid questionnaire. The Dissemination of the Look AHEAD Weight Management Treatment in the Military (Fit Blue) study used the HUI system to assess the health status of its participants in US Military. HUI system assesses health status in 14 different domains (6 in HUI2 and 8 domains in HUI3) through a complicated utilization of a subset of 41 questions for each domain, and there is no readily available software that takes the raw data and computes the final scores of each domain as well as the corresponding multi-attribute utility function scores and single-attribute utility function scores to compare the health status of a given participant in a given health domain with healthy counterparts in the general population. In this study, we present a SAS ® Macro called %HUI that receives the raw HUI data and computes all domain scores as well as utility scores. We have tested the %HUI macro with the test data provided in the HUI manual and applied it to the HUI data from the Fit Blue study.
{"title":"A SAS macro to compute HUI summary and utility scores: An application to the Fit Blue study","authors":"M. Koçak, Jiajing Wang, R. Krukowski, W. Talcott, R. Klesges","doi":"10.1080/25742558.2019.1649788","DOIUrl":"https://doi.org/10.1080/25742558.2019.1649788","url":null,"abstract":"Abstract The Health Utilities Index (HUI) questionnaire provides a mechanism to assess intervention effectiveness in multi-attribute health-related quality of life utilizing a set of health status classification systems. It is a comprehensive and valid questionnaire. The Dissemination of the Look AHEAD Weight Management Treatment in the Military (Fit Blue) study used the HUI system to assess the health status of its participants in US Military. HUI system assesses health status in 14 different domains (6 in HUI2 and 8 domains in HUI3) through a complicated utilization of a subset of 41 questions for each domain, and there is no readily available software that takes the raw data and computes the final scores of each domain as well as the corresponding multi-attribute utility function scores and single-attribute utility function scores to compare the health status of a given participant in a given health domain with healthy counterparts in the general population. In this study, we present a SAS ® Macro called %HUI that receives the raw HUI data and computes all domain scores as well as utility scores. We have tested the %HUI macro with the test data provided in the HUI manual and applied it to the HUI data from the Fit Blue study.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1649788","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45823226","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 : 2019-01-01DOI: 10.1080/25742558.2019.1596553
E. Oral, Ece Oral
Abstract In the manuscript entitled "A Robust Unbiased Dual to Product Estimator for Population Mean through Modified Maximum Likelihood in Simple Random Sampling", several publications and derivations which belong to E. Oral were used without sufficient acknowledgment or citation. In this paper, we comment on the manuscript, and refer the reader to the original sources of the derivations and publications.
{"title":"Commentary on S. Kumar and P. Chhaparwal, 2016. A robust unbiased dual to product estimator for population mean through Modified Maximum Likelihood in simple random sampling, Cogent Mathematics, 3:1168070","authors":"E. Oral, Ece Oral","doi":"10.1080/25742558.2019.1596553","DOIUrl":"https://doi.org/10.1080/25742558.2019.1596553","url":null,"abstract":"Abstract In the manuscript entitled \"A Robust Unbiased Dual to Product Estimator for Population Mean through Modified Maximum Likelihood in Simple Random Sampling\", several publications and derivations which belong to E. Oral were used without sufficient acknowledgment or citation. In this paper, we comment on the manuscript, and refer the reader to the original sources of the derivations and publications.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1596553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60142278","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 : 2019-01-01DOI: 10.1080/25742558.2019.1596552
D. Satoh
Abstract Behaviour of the upper limit estimated by an unsuitable model (the logistic curve model) was mathematically analysed for data on an exact solution of the Gompertz curve model with integrable difference equations. The analysis contributes to identifying a suitable model because the behaviour is independent of noise included in actual data. A suitable model is indispensable for correct forecasts. The following results were proved. The estimated upper limit monotonically increases as the data size increases and converges to the upper limit estimated with the suitable model (the Gompertz curve model) as the data size approaches infinity. Therefore, the upper limit estimated with the logistic curve model is smaller than that estimated with the Gompertz curve model.
{"title":"Properties of Gompertz data revealed with non-Gompertz integrable difference equation","authors":"D. Satoh","doi":"10.1080/25742558.2019.1596552","DOIUrl":"https://doi.org/10.1080/25742558.2019.1596552","url":null,"abstract":"Abstract Behaviour of the upper limit estimated by an unsuitable model (the logistic curve model) was mathematically analysed for data on an exact solution of the Gompertz curve model with integrable difference equations. The analysis contributes to identifying a suitable model because the behaviour is independent of noise included in actual data. A suitable model is indispensable for correct forecasts. The following results were proved. The estimated upper limit monotonically increases as the data size increases and converges to the upper limit estimated with the suitable model (the Gompertz curve model) as the data size approaches infinity. Therefore, the upper limit estimated with the logistic curve model is smaller than that estimated with the Gompertz curve model.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1596552","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45166007","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 : 2019-01-01DOI: 10.1080/25742558.2019.1588191
I. Tzeng, Li-Shya Chen
Abstract The sample moment can be used to estimate the population third central moment, , in the Johnson’s modified t-statistic for skewed distributions. However, moment estimator is non-unique and insufficient for the parameter of population. In this paper, we display the maximum likelihood estimator (MLE) of in modified t-statistic as parent distributions are asymmetrical. A Monte Carlo study shows that the MLE procedure is more powerful than Student’s t-test and ordinary Johnson’s modified t-test for a variety of positively skewed distributions with small sample sizes.
{"title":"Testing the mean of skewed distributions applying the maximum likelihood estimator","authors":"I. Tzeng, Li-Shya Chen","doi":"10.1080/25742558.2019.1588191","DOIUrl":"https://doi.org/10.1080/25742558.2019.1588191","url":null,"abstract":"Abstract The sample moment can be used to estimate the population third central moment, , in the Johnson’s modified t-statistic for skewed distributions. However, moment estimator is non-unique and insufficient for the parameter of population. In this paper, we display the maximum likelihood estimator (MLE) of in modified t-statistic as parent distributions are asymmetrical. A Monte Carlo study shows that the MLE procedure is more powerful than Student’s t-test and ordinary Johnson’s modified t-test for a variety of positively skewed distributions with small sample sizes.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1588191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48021486","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 : 2019-01-01DOI: 10.1080/25742558.2019.1695437
Hiroshi Shiraishi
Abstract We derive the Local Asymptotic Normality (LAN) property for a multivariate generalized integer-valued autoregressive (MGINAR) process with order p. The generalized thinning operator in the MGINAR(p) process includes not only the usual Binomial thinning but also Poisson thinning, geometric thinning, Negative Binomial thinning and so on. By using the LAN property, we propose an efficient estimation method for the parameter of the MGINAR(p) process. Our procedure is based on the one-step method, which update initial -consistent estimators to efficient ones. The one-step method has advantages in both computational simplicity and efficiency. Some numerical results for the asymptotic relative efficiency (ARE) of our estimators and the CLS estimators are presented. In addition, a real data analysis is provided to illustrate the application of the proposed estimation method.
{"title":"Local asymptotic normality and efficient estimation for multivariate GINAR(p) models","authors":"Hiroshi Shiraishi","doi":"10.1080/25742558.2019.1695437","DOIUrl":"https://doi.org/10.1080/25742558.2019.1695437","url":null,"abstract":"Abstract We derive the Local Asymptotic Normality (LAN) property for a multivariate generalized integer-valued autoregressive (MGINAR) process with order p. The generalized thinning operator in the MGINAR(p) process includes not only the usual Binomial thinning but also Poisson thinning, geometric thinning, Negative Binomial thinning and so on. By using the LAN property, we propose an efficient estimation method for the parameter of the MGINAR(p) process. Our procedure is based on the one-step method, which update initial -consistent estimators to efficient ones. The one-step method has advantages in both computational simplicity and efficiency. Some numerical results for the asymptotic relative efficiency (ARE) of our estimators and the CLS estimators are presented. In addition, a real data analysis is provided to illustrate the application of the proposed estimation method.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1695437","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46876294","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 : 2019-01-01DOI: 10.1080/25742558.2019.1684228
Maha F. Sewailem, A. Baklizi
Abstract The primary aim of this study is to explore and investigate the maximum likelihood (ML) estimation and the Bayesian approach to estimating the parameters of log-logistic distribution and to calculate the approximate intervals for the parameters and the survival function based on adaptive progressive type-II censored data. The ML estimators of the parameters of the probability distribution were obtained via the Newton–Raphson Method. The approximate confidence intervals for the reliability function were calculated using the delta method. The Bayes estimators based on squared error loss function (SELF) and the approximate credible intervals for the unknown parameters and the survival function using the Bayesian approach were constructed using the Markov Chain Monte Carlo (MCMC) method. A Monte Carlo study was performed to examine the proposed methods under different situations, based on mean-squared error, bias, coverage probability, and expected length-estimated criteria. The Bayesian approach appears to be better than the likelihood for estimating the log-logistic model parameters. An application to real data was included.
{"title":"Inference for the log-logistic distribution based on an adaptive progressive type-II censoring scheme","authors":"Maha F. Sewailem, A. Baklizi","doi":"10.1080/25742558.2019.1684228","DOIUrl":"https://doi.org/10.1080/25742558.2019.1684228","url":null,"abstract":"Abstract The primary aim of this study is to explore and investigate the maximum likelihood (ML) estimation and the Bayesian approach to estimating the parameters of log-logistic distribution and to calculate the approximate intervals for the parameters and the survival function based on adaptive progressive type-II censored data. The ML estimators of the parameters of the probability distribution were obtained via the Newton–Raphson Method. The approximate confidence intervals for the reliability function were calculated using the delta method. The Bayes estimators based on squared error loss function (SELF) and the approximate credible intervals for the unknown parameters and the survival function using the Bayesian approach were constructed using the Markov Chain Monte Carlo (MCMC) method. A Monte Carlo study was performed to examine the proposed methods under different situations, based on mean-squared error, bias, coverage probability, and expected length-estimated criteria. The Bayesian approach appears to be better than the likelihood for estimating the log-logistic model parameters. An application to real data was included.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1684228","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45494235","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 : 2019-01-01DOI: 10.1080/25742558.2019.1702860
Shahram Banaei, A. Samadi
Abstract In this paper, by applying a measure of noncompactness in the space L∞(ℝn) and a new generalization of Darbo fixed point theorem, we study the existence of solutions for a class of the system of integral equations. Our main result is more general than the main result of [2]. Finally, an example is presented to show the usefulness of the outcome.
{"title":"Application of measures of noncompactness to the system of integral equations","authors":"Shahram Banaei, A. Samadi","doi":"10.1080/25742558.2019.1702860","DOIUrl":"https://doi.org/10.1080/25742558.2019.1702860","url":null,"abstract":"Abstract In this paper, by applying a measure of noncompactness in the space L∞(ℝn) and a new generalization of Darbo fixed point theorem, we study the existence of solutions for a class of the system of integral equations. Our main result is more general than the main result of [2]. Finally, an example is presented to show the usefulness of the outcome.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1702860","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47837605","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 : 2019-01-01DOI: 10.1080/25742558.2019.1612614
Mohamed A. Zaitri, Mohand Ouamer Bibi, Mohand Bentobache
Abstract In this paper, we present an algorithm for finding an approximate numerical solution for linear optimal control problems. This algorithm is based on the hybrid direction algorithm developed by Bibi and Bentobache [A hybrid direction algorithm for solving linear programs, International Journal of Computer Mathematics, vol. 92, no.1, pp. 201–216, 2015]. We define an optimality estimate and give a necessary and sufficient condition to characterize the optimality of a certain admissible control of the discretized problem, then we give a numerical example to illustrate the proposed approach. Finally, we present some numerical results which show the convergence of the proposed algorithm to the optimal solution of the presented continuous optimal control problem.
摘要本文给出了线性最优控制问题的近似数值解的一种算法。该算法基于Bibi和Bentobache提出的混合方向算法[A hybrid direction algorithm for solving linear programs, International Journal of Computer Mathematics, vol. 92, no. 5]。1, pp. 201-216, 2015]。我们定义了最优性估计，给出了离散化问题的某一可容许控制的最优性的充分必要条件，并给出了一个数值例子来说明所提出的方法。最后给出了一些数值结果，证明了所提算法对所提连续最优控制问题的最优解的收敛性。
{"title":"A hybrid direction algorithm for solving optimal control problems","authors":"Mohamed A. Zaitri, Mohand Ouamer Bibi, Mohand Bentobache","doi":"10.1080/25742558.2019.1612614","DOIUrl":"https://doi.org/10.1080/25742558.2019.1612614","url":null,"abstract":"Abstract In this paper, we present an algorithm for finding an approximate numerical solution for linear optimal control problems. This algorithm is based on the hybrid direction algorithm developed by Bibi and Bentobache [A hybrid direction algorithm for solving linear programs, International Journal of Computer Mathematics, vol. 92, no.1, pp. 201–216, 2015]. We define an optimality estimate and give a necessary and sufficient condition to characterize the optimality of a certain admissible control of the discretized problem, then we give a numerical example to illustrate the proposed approach. Finally, we present some numerical results which show the convergence of the proposed algorithm to the optimal solution of the presented continuous optimal control problem.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1612614","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43694132","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}
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