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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. Robust testing of general linear hypotheses on the regression coefficients are proposed using the new estimators. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study.'
author:
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    Castilla, E.$^{1}$; Ghosh, A$^{2}$; Martin, N.$^{1}$ and Pardo, L.$^{1}$\
    $^{1}$[Complutense University of Madrid, Madrid, Spain]{}\
    $^{2}$[Indian Statistical Institute, Kolkata, India]{}
title: '**Robust semiparametric inference for polytomous logistic regression with complex survey design**'
---

**Keywords**[: Cluster sampling; Design effect; Minimum quasi weighted DPD estimator; Polytomous logistic regression model; Pseudo minimum phi-divergence estimator; Quasi-likelihood; Robustness]{}

Introduction\[sec1\]
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In many real-life applications, we come across data that have been collected through a complex survey scheme, like stratified sampling or cluster 