First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t-distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.
首先，我们研究了边际分布为 Student t 分布的分数 Ornstein-Uhlenbeck 过程中漂移参数的估计。我们得到了基于斯皮尔曼相关性的漂移参数估计器、量子估计器和基于布朗偏移的估计器。然后，我们研究了分数反高斯和分数伽马奥恩斯坦-乌伦贝克过程中的矩估计方法和量估计方法。
{"title":"Quantile estimation in fractional Levy Ornstein-Uhlenbeck processes","authors":"Jaya P.N. Bishwal","doi":"10.3233/mas-221427","DOIUrl":"https://doi.org/10.3233/mas-221427","url":null,"abstract":"First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t-distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139154608","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}
This paper investigates the moments of a stochastic process that satisfies the one-dimensional linear stochastic differential equation (SDE) with nonlinear time-dependent drift and diffusion coefficients. The goal is to derive formulas for the nth exact moment, that instead of seeking the transition density function by solving the Fokker-Plank equations or moment-generating functions, which can be difficult to solve in closed form. We will appropriately apply Itô’s formula and the properties of the Wiener process with a constant drift and diffusion term, which is a Gaussian process to obtain the exact higher-order moments.
{"title":"Exact higher-order moments for linear non-homogeneous stochastic differential equation","authors":"A. Guidoum, Kamal Boukhetala","doi":"10.3233/mas-231435","DOIUrl":"https://doi.org/10.3233/mas-231435","url":null,"abstract":"This paper investigates the moments of a stochastic process that satisfies the one-dimensional linear stochastic differential equation (SDE) with nonlinear time-dependent drift and diffusion coefficients. The goal is to derive formulas for the nth exact moment, that instead of seeking the transition density function by solving the Fokker-Plank equations or moment-generating functions, which can be difficult to solve in closed form. We will appropriately apply Itô’s formula and the properties of the Wiener process with a constant drift and diffusion term, which is a Gaussian process to obtain the exact higher-order moments.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139153843","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}
In survey sampling, it is observed that researchers and users of statistics sometimes do not take into consideration the tool that will be most appropriate for the measure of location. As a result, they often go for the mean or total, which has wider coverage in the finite population sampling literature, unlike the median, which is more complicated to deal with given that it has to do with ordered data. Keeping in mind the established facts from the literature on the usefulness of the median estimator in estimating economic indicators for high precision and efficiency, this study has made useful improvement in estimating the population median not only for gains in efficiency but also in achieving less biased estimates. The study suggests an estimator of population median in single and double sampling techniques. In addition, minimum mean square error has also been obtained for a given cost function under double sampling. Results obtained from both theoretical and empirical investigations reveal that the proposed estimators perform better when the considered variables are from a highly skewed distribution, such as income, expenditure, scores, etc. Moreso, it is observed that the proposed estimators compete favorably with less bias and outstanding gains in efficiency than the existing estimators of its class. In addition, this study avails us of an appropriate way of constructing the cost function for better evaluations compared to an existing estimator considered in this work.
{"title":"Model formulation on efficiency for median estimation under a fixed cost in survey sampling","authors":"M. Iseh","doi":"10.3233/mas-231437","DOIUrl":"https://doi.org/10.3233/mas-231437","url":null,"abstract":"In survey sampling, it is observed that researchers and users of statistics sometimes do not take into consideration the tool that will be most appropriate for the measure of location. As a result, they often go for the mean or total, which has wider coverage in the finite population sampling literature, unlike the median, which is more complicated to deal with given that it has to do with ordered data. Keeping in mind the established facts from the literature on the usefulness of the median estimator in estimating economic indicators for high precision and efficiency, this study has made useful improvement in estimating the population median not only for gains in efficiency but also in achieving less biased estimates. The study suggests an estimator of population median in single and double sampling techniques. In addition, minimum mean square error has also been obtained for a given cost function under double sampling. Results obtained from both theoretical and empirical investigations reveal that the proposed estimators perform better when the considered variables are from a highly skewed distribution, such as income, expenditure, scores, etc. Moreso, it is observed that the proposed estimators compete favorably with less bias and outstanding gains in efficiency than the existing estimators of its class. In addition, this study avails us of an appropriate way of constructing the cost function for better evaluations compared to an existing estimator considered in this work.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139153352","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}
A two-parameter quasi Rama distribution which contains the Rama distribution as particular case has been proposed. Its statistical properties based on moments have been discussed. The hazard rate function, mean residual life function, mean deviations and stochastic ordering of the distribution have been derived and studied. The estimation of parameters using method of moments and maximum likelihood methods has been discussed. A simulation study has been presented to know the performance of maximum likelihood estimates. The goodness of fit of the proposed distribution on two datasets relating to failure times has been presented.
{"title":"A quasi Rama distribution","authors":"Rama Shanker, Hrittika Das, Kamlesh Kumar Shukla","doi":"10.3233/mas-221417","DOIUrl":"https://doi.org/10.3233/mas-221417","url":null,"abstract":"A two-parameter quasi Rama distribution which contains the Rama distribution as particular case has been proposed. Its statistical properties based on moments have been discussed. The hazard rate function, mean residual life function, mean deviations and stochastic ordering of the distribution have been derived and studied. The estimation of parameters using method of moments and maximum likelihood methods has been discussed. A simulation study has been presented to know the performance of maximum likelihood estimates. The goodness of fit of the proposed distribution on two datasets relating to failure times has been presented.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343622","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}
In a classification scenario, we usually come across data with and without class labels. If the class labels of individuals are unknown or masked by hidden components, the classifier rules must include the identification of the actual number of subcomponents in the data. Also, the presence of measurement errors in the data may influence the measures of the receiver operating characteristic model. In this paper, a mixture of multivariate receiver operating characteristic models is proposed to deal with multi-model patterns in the data, and a bias-corrected estimator is derived for estimating the area under the curve of the proposed model. The proposed methodology is supported by the real dataset and simulation studies.
{"title":"Estimating the AUC of mixture MROC curve in the presence of measurement errors","authors":"G. Siva, Vishnu Vardhan R., Christophe Chesneau","doi":"10.3233/mas-231432","DOIUrl":"https://doi.org/10.3233/mas-231432","url":null,"abstract":"In a classification scenario, we usually come across data with and without class labels. If the class labels of individuals are unknown or masked by hidden components, the classifier rules must include the identification of the actual number of subcomponents in the data. Also, the presence of measurement errors in the data may influence the measures of the receiver operating characteristic model. In this paper, a mixture of multivariate receiver operating characteristic models is proposed to deal with multi-model patterns in the data, and a bias-corrected estimator is derived for estimating the area under the curve of the proposed model. The proposed methodology is supported by the real dataset and simulation studies.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343623","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}
Lahiru Wickramasinghe, Alexandre Leblanc, Saman Muthukumarana
We develop a Bayesian approach for estimating multinomial cell probabilities using a smoothed Dirichlet prior. The most important feature of the smoothed Dirichlet prior is that it forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet prior. We propose a shrinkage-type estimator using this Bayesian approach to estimate multinomial cell probabilities. The proposed estimator allows us to borrow information across other multinomial populations and cell categories simultaneously to improve the estimation of cell probabilities, especially in a context of sparsity with ordered categories. We demonstrate the proposed approach using COVID-19 data and estimate the distribution of positive COVID-19 cases across age groups for Canadian health regions. Our approach allows improved estimation in smaller health regions where few cases have been observed.
{"title":"Bayesian inference on sparse multinomial data using smoothed Dirichlet distribution with an application to COVID-19 data","authors":"Lahiru Wickramasinghe, Alexandre Leblanc, Saman Muthukumarana","doi":"10.3233/mas-221411","DOIUrl":"https://doi.org/10.3233/mas-221411","url":null,"abstract":"We develop a Bayesian approach for estimating multinomial cell probabilities using a smoothed Dirichlet prior. The most important feature of the smoothed Dirichlet prior is that it forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet prior. We propose a shrinkage-type estimator using this Bayesian approach to estimate multinomial cell probabilities. The proposed estimator allows us to borrow information across other multinomial populations and cell categories simultaneously to improve the estimation of cell probabilities, especially in a context of sparsity with ordered categories. We demonstrate the proposed approach using COVID-19 data and estimate the distribution of positive COVID-19 cases across age groups for Canadian health regions. Our approach allows improved estimation in smaller health regions where few cases have been observed.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343729","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}
Jorge Alberto Achcar, Emerson Barili, Edson Zangiacomi Martinez
The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology.
{"title":"Semiparametric transformation model:A hierarchical Bayesian approach","authors":"Jorge Alberto Achcar, Emerson Barili, Edson Zangiacomi Martinez","doi":"10.3233/mas-221408","DOIUrl":"https://doi.org/10.3233/mas-221408","url":null,"abstract":"The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343727","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}
In this study, we utilized a best-worst scaling experiment design to assess the potential factors associated with depression, anxiety, and stress among health professionals following the experience of the COVID-19 pandemic. The maximum difference model was performed to analyze the potential risk factors associated with depression, anxiety, and stress. As a case study, a total of 300 health professionals in Ghana were included in the survey. The majority, 112 (68.7%) male health professionals and 97 (70.8%) female health professionals reported that they had encountered suspected COVID-19 patients. 83 (50.9%) of the male health professionals and 76 (55.5%) of the female health professionals reported that they had encountered confirmed COVID-19 patients. A considerable proportion of the males 59 (36.2%) and females 57 (41.6%) health professionals reported coming into direct contact with COVID-19 lab specimens. The findings indicated that a high proportion of health professionals encountered suspected or confirmed COVID-19 patients, while a considerable proportion had direct contact with COVID-19 lab specimens leading to psychological problems. Risk factors such as contact with confirmed COVID-19 patients, the relentless spread of the coronavirus, death of patients and colleagues, shortage of medical protective equipment, direct contact with COVID-19 lab specimens, and the permanent threat of being infected should be given special attention, and necessary psychological intervention provided for health professionals endorsing these risk factors. Improving the supply of medical protective equipment to meet occupational protection practices, sufficient rest, and improving the vaccination of the population might help safeguard health professionals from depression, anxiety, and stress. Our results provide insight into policy discussions on the mental health of health professionals and interventions that are essential to enhance psychological resilience.
{"title":"Best-worst scaling in studying the impact of the coronavirus pandemic on health professionals in Ghana","authors":"Eric Nyarko, Dennis Arku, Gifty Duah","doi":"10.3233/mas-221398","DOIUrl":"https://doi.org/10.3233/mas-221398","url":null,"abstract":"In this study, we utilized a best-worst scaling experiment design to assess the potential factors associated with depression, anxiety, and stress among health professionals following the experience of the COVID-19 pandemic. The maximum difference model was performed to analyze the potential risk factors associated with depression, anxiety, and stress. As a case study, a total of 300 health professionals in Ghana were included in the survey. The majority, 112 (68.7%) male health professionals and 97 (70.8%) female health professionals reported that they had encountered suspected COVID-19 patients. 83 (50.9%) of the male health professionals and 76 (55.5%) of the female health professionals reported that they had encountered confirmed COVID-19 patients. A considerable proportion of the males 59 (36.2%) and females 57 (41.6%) health professionals reported coming into direct contact with COVID-19 lab specimens. The findings indicated that a high proportion of health professionals encountered suspected or confirmed COVID-19 patients, while a considerable proportion had direct contact with COVID-19 lab specimens leading to psychological problems. Risk factors such as contact with confirmed COVID-19 patients, the relentless spread of the coronavirus, death of patients and colleagues, shortage of medical protective equipment, direct contact with COVID-19 lab specimens, and the permanent threat of being infected should be given special attention, and necessary psychological intervention provided for health professionals endorsing these risk factors. Improving the supply of medical protective equipment to meet occupational protection practices, sufficient rest, and improving the vaccination of the population might help safeguard health professionals from depression, anxiety, and stress. Our results provide insight into policy discussions on the mental health of health professionals and interventions that are essential to enhance psychological resilience.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343620","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}
This paper proposes a new classification model using the Bayes method. This model not only determines the prior probability based on the k-means algorithm, builds the method for estimating the probability density function via the kernel function, but also classifies the objects to the known populations. The proposed model is described via the experiment of image classifying. In this example, we first use the Gray level co-occurrence matrix to extract the features of images, and next classify this data set based on the improved Bayesian method. In another application, we also build the classification problem for the Algerian Forest Fires data set. The outstanding advantages of this method are the adaptive ability of the kernel function, the classification for multi-class, and the reduction of computational costs. In addition, the experimental results also show the potential of the developed model.
{"title":"Multi-class classification using a new Bayesian method","authors":"Tai Vovan, Hieu Nguyenthikim, Dinh Phamtoan","doi":"10.3233/mas-221428","DOIUrl":"https://doi.org/10.3233/mas-221428","url":null,"abstract":"This paper proposes a new classification model using the Bayes method. This model not only determines the prior probability based on the k-means algorithm, builds the method for estimating the probability density function via the kernel function, but also classifies the objects to the known populations. The proposed model is described via the experiment of image classifying. In this example, we first use the Gray level co-occurrence matrix to extract the features of images, and next classify this data set based on the improved Bayesian method. In another application, we also build the classification problem for the Algerian Forest Fires data set. The outstanding advantages of this method are the adaptive ability of the kernel function, the classification for multi-class, and the reduction of computational costs. In addition, the experimental results also show the potential of the developed model.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343621","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}
A new parametric regression model is developed based on the gamma-Maxwell distribution. Monte Carlo simulations show the accuracy of the maximum likelihood estimators. The proposed model explains COVID-19 mortality rates of the 50 U.S. largest cities.
{"title":"The gamma-Maxwell regression for COVID-19 mortality rates of the 50 U.S. largest cities","authors":"N.S.S. da Costa, G.M. Cordeiro","doi":"10.3233/mas-221419","DOIUrl":"https://doi.org/10.3233/mas-221419","url":null,"abstract":"A new parametric regression model is developed based on the gamma-Maxwell distribution. Monte Carlo simulations show the accuracy of the maximum likelihood estimators. The proposed model explains COVID-19 mortality rates of the 50 U.S. largest cities.","PeriodicalId":35000,"journal":{"name":"Model Assisted Statistics and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343728","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：