A family of shrinkage estimators for the square of mean in normal distribution

Abstract

This paper is devoted to the problem of estimating the square of population mean (μ²) in normal distribution when a prior estimate or guessed value σ₀ ² of the population variance σ² is available. We have suggested a family of shrinkage estimators ${\mathop T\limits^*} _{(p)}$, say, for μ² with its mean squared error formula. A condition is obtained in which the suggested estimator ${\mathop T\limits^*} _{(p)}$ is more efficient than Srivastava et al’s (1980) estimator T_min. Numerical illustrations have been carried out to demonstrate the merits of the constructed estimator ${\mathop T\limits^*} _{(p)}$ over T_min. It is observed that some of these estimators offer improvements over T_min particularly when the population is heterogeneous and σ² is in the vicinity of σ₀ ².