Equivalence Of The problem And The Regression Problem with one Nuisance Parameter

In this paper, we study the estimation of the unknown mean parameter ŋ of a univariate normal distribution when the variance is known σ^2=1 of size one. The main estimation methods have been discussed along with their properties and the properties of the estimators. The focus is concentrated on the shrinkage method for finding the estimators. We wish to prove that there is a relationship between the shrinkage estimator b (the estimator of the parameter vector β in the linear regression model) and η; of A (η,1), where for each estimator 1(x)=X{x)x for /V(η;,l) problem, there will be a corresponding WALS (weighted average least squares) estimator in the regression problem of the form b=X(η)b+(1-X(η)b.