{"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}
Kouakou Mathias Amani, Ouagnina Hili, Konan Jean Geoffroy Kouakou
{"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}
Narayanaswamy Balakrishnan, Jan Rychtář, Dewey Taylor
{"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}
{"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}
{"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}
{"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}
{"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}
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}
{"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}
{"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}