In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might occur, that does not demonstrate the true condition of the response process. In contrast with binary outcome by which classification error occurs between two categories, disorderliness in categorical outcome has more intricate impacts, as a result of the increased number of categories and asymmetric miscategorization matrix. When no modification is made, insensitivity of errors in either covariate or response variable, results in potentially incorrect conclusion, tends to bias the statistical inference and eventually degrades the efficiency of the decision-making procedure. In this article, we provide an approach to simultaneously adjust for misclassification in the correlated nominal response and measurement error in the covariates, incorporating validation data in the estimation of misclassification probabilities, using the multivariate Gauss–Hermite quadrature technique for the approximation of the likelihood function. Simulation results demonstrate the effects of modifying covariate measurement error and response misclassification on the estimation procedure.
{"title":"Validation Data-Located Modification for the Multilevel Analysis of Miscategorized Nominal Response with Covariates Subject to Measurement Error","authors":"Maryam Ahangari, Mousa Golalizadeh, Zahra Rezaei Ghahroodi","doi":"10.3103/s1066530723040026","DOIUrl":"https://doi.org/10.3103/s1066530723040026","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might occur, that does not demonstrate the true condition of the response process. In contrast with binary outcome by which classification error occurs between two categories, disorderliness in categorical outcome has more intricate impacts, as a result of the increased number of categories and asymmetric miscategorization matrix. When no modification is made, insensitivity of errors in either covariate or response variable, results in potentially incorrect conclusion, tends to bias the statistical inference and eventually degrades the efficiency of the decision-making procedure. In this article, we provide an approach to simultaneously adjust for misclassification in the correlated nominal response and measurement error in the covariates, incorporating validation data in the estimation of misclassification probabilities, using the multivariate Gauss–Hermite quadrature technique for the approximation of the likelihood function. Simulation results demonstrate the effects of modifying covariate measurement error and response misclassification on the estimation procedure.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"24 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029452","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 : 2023-12-23DOI: 10.3103/s1066530723040038
Kouakou Mathias Amani, Ouagnina Hili, Konan Jean Geoffroy Kouakou
Abstract
The marginalized zero-inflated poisson (MZIP) regression model quantifies the effects of an explanatory variable in the mixture population. Also, in practice the variables are usually partially observed. Thus, we first propose to study the maximum likelihood estimator when all variables are observed. Then, assuming that the probability of selection is modeled using mixed covariates (continuous, discrete and categorical), we propose a semiparametric inverse-probability weighted (SIPW) method for estimating the parameters of the MZIP model with covariates missing at random (MAR). The asymptotic properties (consistency, asymptotic normality) of the proposed estimators are established under certain regularity conditions. Through numerical studies, the performance of the proposed estimators was evaluated. Then the results of the SIPW are compared to the results obtained by semiparametric inverse-probability weighted kermel-based (SIPWK) estimator method. Finally, we apply our methodology to a dataset on health care demand in the United States.
{"title":"Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates","authors":"Kouakou Mathias Amani, Ouagnina Hili, Konan Jean Geoffroy Kouakou","doi":"10.3103/s1066530723040038","DOIUrl":"https://doi.org/10.3103/s1066530723040038","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The marginalized zero-inflated poisson (MZIP) regression model\u0000quantifies the effects of an explanatory variable in the mixture\u0000population. Also, in practice the variables are usually partially\u0000observed. Thus, we first propose to study the maximum likelihood\u0000estimator when all variables are observed. Then, assuming that the\u0000probability of selection is modeled using mixed covariates\u0000(continuous, discrete and categorical), we propose a\u0000semiparametric inverse-probability weighted (SIPW) method for\u0000estimating the parameters of the MZIP model with covariates\u0000missing at random (MAR). The asymptotic properties (consistency,\u0000asymptotic normality) of the proposed estimators are established\u0000under certain regularity conditions. Through numerical studies,\u0000the performance of the proposed estimators was evaluated. Then the\u0000results of the SIPW are compared to the results obtained by\u0000semiparametric inverse-probability weighted kermel-based (SIPWK)\u0000estimator method. Finally, we apply our methodology to a dataset\u0000on health care demand in the United States.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"28 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029447","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 : 2023-12-23DOI: 10.3103/s106653072304004x
Narayanaswamy Balakrishnan, Jan Rychtář, Dewey Taylor
Abstract
We propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios. We show that our method provides a nearly unbiased estimator for the non-parametric skewness measure. We empirically evaluate the performance on real-life data sets of COVID-19 vaccination status. We also demonstrate how the method can be applied to detect the skewness of the underlying distribution.
{"title":"Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality","authors":"Narayanaswamy Balakrishnan, Jan Rychtář, Dewey Taylor","doi":"10.3103/s106653072304004x","DOIUrl":"https://doi.org/10.3103/s106653072304004x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios. We show that our method provides a nearly unbiased estimator for the non-parametric skewness measure. We empirically evaluate the performance on real-life data sets of COVID-19 vaccination status. We also demonstrate how the method can be applied to detect the skewness of the underlying distribution.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"3 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029806","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 : 2023-09-01DOI: 10.3103/s1066530723030031
Sam Efromovich
{"title":"Sharp Lower Bound for Regression with Measurement Errors and Its Implication for Ill-Posedness of Functional Regression","authors":"Sam Efromovich","doi":"10.3103/s1066530723030031","DOIUrl":"https://doi.org/10.3103/s1066530723030031","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135388530","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 : 2023-09-01DOI: 10.3103/s106653072303002x
Manoj Chacko, Annie Grace
{"title":"Information Generating Function of $$boldsymbol{k}$$-Record Values and Its Applications","authors":"Manoj Chacko, Annie Grace","doi":"10.3103/s106653072303002x","DOIUrl":"https://doi.org/10.3103/s106653072303002x","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135388536","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 : 2023-09-01DOI: 10.3103/s1066530723030043
Xiangyu Han, Chuancun Yin
{"title":"Multivariate Doubly Truncated Moments for a Class of Multivariate Location-Scale Mixture of Elliptical Distributions","authors":"Xiangyu Han, Chuancun Yin","doi":"10.3103/s1066530723030043","DOIUrl":"https://doi.org/10.3103/s1066530723030043","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135388526","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 : 2023-09-01DOI: 10.3103/s1066530723030055
F. Hosseini Shekarabi, M. Khodabin
{"title":"Numerical Solution of Stochastic Mixed Volterra–Fredholm Integral Equations Driven by Space-Time Brownian Motion via Two-Dimensional Triangular Functions","authors":"F. Hosseini Shekarabi, M. Khodabin","doi":"10.3103/s1066530723030055","DOIUrl":"https://doi.org/10.3103/s1066530723030055","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135388531","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 : 2023-06-01DOI: 10.3103/S1066530723020011
Mamadou Aliou Barry, E. Deme, A. Diop, S. MANOU-ABI
{"title":"Improved Estimators of Tail Index and Extreme Quantiles under Dependence Serials","authors":"Mamadou Aliou Barry, E. Deme, A. Diop, S. MANOU-ABI","doi":"10.3103/S1066530723020011","DOIUrl":"https://doi.org/10.3103/S1066530723020011","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"32 1","pages":"133 - 153"},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48774958","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 : 2023-06-01DOI: 10.3103/S1066530723020023
Y. Dijoux
{"title":"Distributions Derived from the Continuous Iteration of the Hyperbolic Sine Function","authors":"Y. Dijoux","doi":"10.3103/S1066530723020023","DOIUrl":"https://doi.org/10.3103/S1066530723020023","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"32 1","pages":"103 - 121"},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47593836","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 : 2023-03-01DOI: 10.3103/S1066530723010040
E. I. A. Sathar, Veena L. Vijayan
{"title":"Quantile Based Geometric Vitality Function of Order Statistics","authors":"E. I. A. Sathar, Veena L. Vijayan","doi":"10.3103/S1066530723010040","DOIUrl":"https://doi.org/10.3103/S1066530723010040","url":null,"abstract":"","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"32 1","pages":"88 - 101"},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44202385","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号