Minimum Divergence Method

This chapter provides a general framework of the minimum divergence method for a statistical model. In particular, we explore the U-minimum divergence method, in which the U-loss function for parameter estimation is introduced as an empirical analogue for the U-divergence given a data set, and the U-estimator is defined by minimizing the U-loss function. The variety of U-estimators is due to the selection diversity of selection for the generator function U. We give a sensible understanding for the dualistic relation of the U-estimator and the maximum U-entropy model. Then, we investigate the robustness performanceRobustness performance of the $$\beta $$ β -power estimator under a typical statistical model that differs from the U-model. Furthermore, the statistical property of the $$\gamma $$ γ -power estimator defined by the projective $$\gamma $$ γ -power divergence is investigated.