Magloire Loudegui Djimdou, Y. Chaubey, Arusharka Sen
{"title":"Distribution of the Joint Survival Function of an Archimedean Copula","authors":"Magloire Loudegui Djimdou, Y. Chaubey, Arusharka Sen","doi":"10.1177/00080683241246438","DOIUrl":"https://doi.org/10.1177/00080683241246438","url":null,"abstract":"Suppose a random vector [Formula: see text] with values in the unit cube has a joint survival function: [Formula: see text] given by an Archimedean copula [Formula: see text] with generator [Formula: see text], a smooth decreasing convex function such that [Formula: see text]. In this article, we provide a formula for the distribution of [Formula: see text] where [Formula: see text] is an independent copy of [Formula: see text] and a method to simulate values from the distribution of Z in the bivariate case, that is, when d = 2. The case d > 2 does not seem to be tractable. As an application, we show how our result can be used to compute the limiting covariance of the empirical Kendall process corresponding to [Formula: see text]. AMS Subject Classification: 62H05","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"48 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141353471","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":"Response Model Selection in Small Area Estimation Under not Missing at Random Nonresponse","authors":"Michael Sverchkov, Danny Pfeffermann","doi":"10.1177/00080683231197291","DOIUrl":"https://doi.org/10.1177/00080683231197291","url":null,"abstract":"Sverchkov and Pfeffermann [16] consider Small Area Estimation (SAE) under informative probability sampling of areas and within the sampled areas, and not missing at random (NMAR) nonresponse. To account for the nonresponse, the authors assume a given response model, which contains the outcome values as one of the covariates and estimate the corresponding response probabilities by application of the Missing Information Principle, which consists of defining the likelihood as if there was complete response and then integrating out the unobserved outcomes from the likelihood by employing the relationship between the distributions of the observed and the missing data. A key condition for the success of this approach is the ‘correct’ specification of the response model. In this article, we consider the likelihood ratio test and information criteria based on the appropriate likelihood and show how they can be used for the selection of the response model. We illustrate the approach by a small simulation study. AMS subject classification: 62D05, 62D10, 62F10","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"17 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136135440","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":"A Bayesian Semi-parametric Modelling Approach for Area Level Small Area Studies","authors":"Marten Thompson, Snigdhansu Chatterjee","doi":"10.1177/00080683231198606","DOIUrl":"https://doi.org/10.1177/00080683231198606","url":null,"abstract":"We present a new semiparametric extension of the Fay-Herriot model, termed the agnostic Fay-Herriot model (AGFH), in which the sampling-level model is expressed in terms of an unknown general function [Formula: see text]. Thus, the AGFH model can express any distribution in the sampling model since the choice of [Formula: see text] is extremely broad. We propose a Bayesian modelling scheme for AGFH where the unknown function [Formula: see text] is assigned a Gaussian Process prior. Using a Metropolis within Gibbs sampling Markov Chain Monte Carlo scheme, we study the performance of the AGFH model, along with that of a hierarchical Bayesian extension of the Fay-Herriot model. Our analysis shows that the AGFH is an excellent modelling alternative when the sampling distribution is non-Normal, especially in the case where the sampling distribution is bounded. It is also the best choice when the sampling variance is high. However, the hierarchical Bayesian framework and the traditional empirical Bayesian framework can be good modelling alternatives when the signal-to-noise ratio is high, and there are computational constraints. AMS subject classification: 62D05; 62F15","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"15 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261803","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":"Disaggregating Health Official Statistics by Integrating Data From Multiple Sources","authors":"Andreea L. Erciulescu","doi":"10.1177/00080683231206629","DOIUrl":"https://doi.org/10.1177/00080683231206629","url":null,"abstract":"Disaggregated statistics help improve the description of the society. However, survey estimates are subject to larger uncertainty at finer levels than at higher levels, and often not even available at fine levels. The Behavioral Risk Factor Surveillance System (BRFSS) is considered the nation’s premier system collecting health data from individuals in the US using telephone surveys. Among the BRFSS official statistics, state-level estimates are available for two related health prevalence quantities: the prevalence of having a personal doctor and the prevalence of having health insurance coverage. No county-level BRFSS estimates are released for these quantities. In addition, county-level estimates for the prevalence of having health insurance coverage are also available from the US. Small Area Health Insurance Estimates (SAHIE) program. This article addresses the disaggregation of the state-level prevalence of having a personal doctor to the county level, by using the state-level relationship between the two BRFSS prevalence variables and the county-level bridge between the BRFSS and the SAHIE prevalence of having health insurance coverage. Using 2018 public-use data, county-level model estimates are produced for both prevalence variables and on both BRFSS and SAHIE scales, improving the usability of the BRFSS public-use data. AMS subject classifications: 62D05, 62H10, 62J05, 62P99","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"SE-10 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135412285","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":"Predicting the Finite Population Distribution Function under a Multilevel Model","authors":"Sumonkanti Das, Nicola Salvati, Ray Chambers","doi":"10.1177/00080683231190258","DOIUrl":"https://doi.org/10.1177/00080683231190258","url":null,"abstract":"Chambers and Dunstan proposed a model-based predictor of the population distribution function that makes use of auxiliary population information under a general sampling design. Subsequently, Rao, Kovar, and Mantel proposed design-based ratio and difference predictors of the population distribution function that also use this auxiliary information. Both predictors (CD and RKM) assume a single level model for the target population. In this article we develop predictors of the finite population distribution function for a population that follows a multilevel model. These new predictors use the same smearing approach underpinning the CD predictor. We compare our new predictors with the CD and RKM predictors via design-based simulation, and show that they perform better than these single level predictors when there is significant intra-cluster correlation. The performances of these new two level predictors are also examined via an empirical study based on data from a large-scale UK business survey aimed at estimating the distribution of hourly pay rates. AMS subject classification: Primary 62G30, Secondary 62G32","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136154363","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":"Rejoinder","authors":"Jae Kwang Kim, Kosuke Morikawa","doi":"10.1177/00080683231183306","DOIUrl":"https://doi.org/10.1177/00080683231183306","url":null,"abstract":"","PeriodicalId":487287,"journal":{"name":"Calcutta Statistical Association Bulletin","volume":"195 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135517260","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}