On Second Order Efficiency of Minimum Discrepancy and Minimum Distance Estimators for the Multinomial Distribution

Abstract

Rao (1961, '62, '63) introduced the concept of second order efficiency (s.o.e.) of an asymptotically efficient i.e., best asymptotically normal (BAN) estimator. The main purpose of introducing this concept was to discriminate different asymptotically efficient estimators. Rao considered some wellknown methods of estimation for the multinomial distribution with true cell probabilities depending on a single unknown parameter. Nagnur and Aithal (1986) obtained a general expression for the s.o.e. of minimum distance estimators, obtained from a particular form of a distance function given by Taylor (1953) for the multinomial distribution . In this paper we have obtained the expression for the s.o.e. of minimum discrepancy (minimum power-divergence) estimators, obtained from a discrepancy function defined by Cressie and Read (1984) . The distance functions and the discrepancy functions which produce estimators having the same s.o.e. have been identified.