Robust semiparametric inference for polytomous logistic regression with complex survey design
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Robust semiparametric inference for polytomous logistic regression with complex survey design Elena Castilla1
· Abhik Ghosh2
· Nirian Martin3
· Leandro Pardo1
Received: 23 October 2019 / Revised: 17 June 2020 / Accepted: 9 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Using the new estimators, robust testing of general linear hypotheses on the regression coefficients are proposed. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study. Keywords Cluster sampling · Design effect · Minimum quasi weighted DPD estimator · Polytomous logistic regression model · Pseudo minimum phi-divergence estimator · Quasi-likelihood · Robustness Mathematics Subject Classification 62J05 · 62F12 · 62F35 · 62H15 · 62F10
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11634020-00430-7) contains supplementary material, which is available to authorized users.
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Nirian Martin [email protected]
1
Interdisciplinary Mathematics Institute and Department of Statistics and O.R, Complutense University of Madrid, 28040 Madrid, Spain
2
Interdisciplinary Statistical Research Unit, Indian Statistical Institute, 700108 Kolkata, India
3
Interdisciplinary Mathematics Institute and Department of Financial, Actuarial Economics and Statistics, Complutense University of Madrid, 28003 Madrid, Spain
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E. Castilla et al.
1 Introduction In several real-life applications, we come across data collected through a complex survey scheme, like stratified or cluster sampling procedure, etc., rather than the simple random sampling. Such situations commonly arise in large scale data collection, for example, within several states of a country or even among different countries. Suitable statistical methods are required to analyze these data by taking care of their stratified structure; this is because there often exist several inter and intra-class correlations within such stratification and ignoring them might lead to erroneous inference. Further, in such a complex survey, if stratified observations are collected on some categorical responses having two or more mutually exclusive unordered categories along with some related covariates, thorough inference about their relationship is of up-most interest for insight generation and policy making. Polytomous logistic regression (PLR) model is a u
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