Estimation of the variance in a normal population after the one-sided pre-test for the mean

Abstract

In this paper, we examine the small sample properties of the pre-test estimator of the variance in a normal population when the alternative hypothesis in the pre-test is one-sided: H₁ :μ > μ₀ where μ is a population mean and μ₀ is any fixed number.It is shown that the optimal critical value of the pre-test based on a certain criterion is [(n-1)/(n+1)]^1/2. It is also shown that the Stein estimator proposed by Stein (1964) is dominated by the pre-test estimator with the optimal critical value if μ ≥ μ₀.

Keywords:

• estimation of variance
• normal population
• one-sided alternative
• pre-test estimator
• Stein estimator