Preliminary Test Estimators and Phi-divergence Measures in Pooling Binomial Data

Two independent random samples are drawn from two Binomial populations with parameters theta1   and   theta2 respectively. Ahmed (1991) considered a preliminary test estimator based on maximum likelihood estimator for estimating theta1   when it is suspected that theta1=theta2.   In this paper we combine minimum phi-divergence estimators as well as phi-divergence test statistics in order to define a preliminary phi-divergence test estimators. These new estimators are compared with the classical estimator as well as the pooled estimator.