MINIMAX REGRET CRITICAL VALUES FOR A PRELIMINARY TEST IN POOLING VARIANCES

Abstract

Suppose we have independent random samples from two normal populations N (μ_i, σ_??_) where the means and the variances are unknown except for the fact that σ_??__??_σ_??_. We wish to estimate the variance of the first population, σ_??_. Then, whether to pool or not to pool two samples is decided via a preliminary F test for equality between the two variances. In this note we discuss the pre-test estimator and seek the optimal critical values for the pre-test, based on a minimax regret criterion. It is shown that the optimal critical values depend on the degrees of freedom and are about 1.7_??_2.8. Also we see that the ordinary (never-pool) estimator of variances is dominated by the pre-test estimator for λ=1.