Abstract:
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The ordinary Bayes estimator based on the posterior density suffers from the potential problems of non-robustness under data contamination or outliers. In this work, we consider the general set-up of independent but non-homogeneous (INH) observations and study a robustified pseudo-posterior based estimation for such parametric INH models. In particular, we focus on a particular robustified posterior, namely R-alpha posterior, developed by Ghosh and Basu (2016) for IID data and later extended by Ghosh and Basu (2017) for INH set-up, where its desirable properties have been illustrated. We have developed Bernstein-von Mises types asymptotic normality results and Laplace type asymptotic expansion of the robust posterior for INH set-up. The robustness of this R-alpha posterior and associated estimators are theoretically examined through influence function analyses. A high breakdown point result is derived for the expected R-alpha posterior estimators of the location parameter under a location-scale type model. Extensive simulations and real life data applications in fixed-design linear regression models numerically illustrate the robustness properties of the pseudo-Bayes estimators.
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