Pitman Performance Of Parameter Estimation In The Linear Model

A meaningful alternative criterion to the mean squared error criterion for comparison of competing estimators of a parameter or parametric function, having received great attention by data analysts and statisticians since 1980's, is Pitman closeness criterion that was introduced by Pitman in 1937.Pitman closeness criterion is used to compare two competing united biased estimators in linear model in the third chapter. United biased estimators include ridge estimator, principal components estimator and many other biased estimators as special cases. We provide a theoretical result about the performance of any two members of a class of united biased estimators and a simulation is performed to illustrate the theoretical results. In particular, some sufficient condition for one estimator being superior to the other is derived.In many practical applications, in addition to the sample information, supplementary information is available that often may be expressed by a linear stochastic restriction. In the forth chapter, Pitman nearness measure of two-stage estimate is given and we prove that under some conditions two-stage estimate is better than least square estimation.Pitman closeness criterion is used to compare united biased estimation with least square estimation in growth curve model in the fifth chapter. A sufficient and necessary condition of which united biased estimation is superior to least square estimator under Pitman closeness criterion is derived, and a Monte Carlo simulation study is performed to illustrate the theoretical results. A sufficient condition for united biased estimation being superior to least square estimator under Pitman closeness criterion is given and some special cases are also considered.