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Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression. (English) Zbl 1349.62087
Summary: 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 [A. Basu et al., Biometrika 85, No. 3, 549–559 (1998; Zbl 0926.62021)]. We establish the asymptotic properties of the proposed estimators, and illustrate the benefits of our method in case of linear regression.

62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
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