On Second Order Efficiency of Estimators Derived by Generalised χ2 Distance Functions

Abstract

Taylor (1953) proposed a distance function in connection with the logit χ2 estimator. For product (associated) multinomial distributions, he showed that minimization of the distance function yields BAN estimators. Aithal (1986) and Rao (1989) considered a modified version of Taylor's distance function and showed that a member belonging to this class leads to a second order efficient estimator. In this paper we consider Taylor's distance function and show that a member belonging to this class produces a second order efficient estimator. In addition to the above two, the m.l. estimator is also second order efficient. In order to compare these three second order efficient estimators, the small sample variances of the estimators are estimated through a simulation study. The results indicate that the variance of the m.l. estimator is the smallest in most of the cases.