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.

在多个社会经济应用中，分析来自复杂调查方案（例如分层或整群抽样）的多态响应非常关键。对于具有如此复杂调查的多方逻辑回归模型，我们提出了一类最小拟加权密度幂散度估计量。该半参数估计器系列是对最大拟加权似然估计器的强大概括，它利用了流行的密度幂散度度量的优点。因此，还得出了设计效果的鲁棒估计量。使用新的估计量，提出了对回归系数进行一般线性假设的稳健检验。