Ordinary and penalized minimum power-divergence estimators in two-way contingency tables

Abstract

Basu and Basu (Statistica Sinica 8:841---860, 1998) have proposed an empty cell penalty for the minimum power-divergence estimators which can lead to improvements in the small sample properties of these estimators. In this paper, we study the small and moderate sample performances of the ordinary and penalized minimum power-divergence estimators in terms of efficiency and robustness for the log-linear models in two-way contingency tables under the assumptions of multinomial sampling. Calculations made by enumerating all possible sample combinations show that the penalized estimators are competitive with the ordinary estimators for the moderate samples and definitely better for the smallest sample considered for both efficiency and robustness under the considered models. The results also reveal that the bigger the main effects the more need for penalization.