On a two stage shrinkage testimator of the mean of a normal distribution

Abstract

Let X be distributed normally with unknown mean μ and known variance σ2. Further, it is assumed that prior knowledge about μ is available in the form of an initial estimate μ0 of μ. It A is proposed to estimate the unknown mean by a testimator that is based upon the result of a test of the hypothesis If H0 is accepted based on the first sample of size n1 we take where the weighing factor k is a function of the test statistic for testing H0. However, if H0 is rejected, we obtain a second sample of size n2, and take . Choosing an expression for the mean square error of is derived and comparisons are made with variance of a single sample mean. The case when the variance σ2 is unknown is also considered.