In real life we often have to deal with situations where the sampled observations are independent and share common parameters in their distribution but are not identically distributed. While the methods based on maximum likelihood provide canonical approaches for doing statistical inference in such contexts, it carries with it the usual baggage of lack of robustness to small deviations from the assumed conditions. In the present paper we develop a general estimation method for handling such situations based on a minimum distance approach which exploits the robustness properties of the density power divergence measure (Basu et al. 1998 [2]). We establish the asymptotic properties of the proposed estimators, and illustrate the benefits of our method in case of linear regression.

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. A family of robust Wald type tests are considered here, where the minimum density power divergence estimator is used instead of the maximum likelihood estimator. We obtain the asymptotic distribution and also study the robustness properties of these Wald type test statistics. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.