[Show abstract][Hide abstract] ABSTRACT: The estimation of the mean vector of a multivariate normal distribution, under the uncertain prior information (UPI) that component means are equal but unknown, is considered. The positive part of Stein-Rule (PSE) and improved preliminary test (IPE) estimators are proposed. It is demonstrated analytically as well as computationally that the positive part of Stein-Rule estimator is superior to the usual Stein-Rule estimator (SE). Furthermore, it is shown that the proposed improved pretest estimator dominates the traditional preliminary test estimator (PE) regardless the correctness of the nonsample information. The relative dominance of the proposed estimators are presented analytically as well as graphically. Percentage improvements of the proposed estimators over the unrestricted estimator (UE) are computed. It is shown that for p⩾3, SE or PSE is the best to use while for p⩽2, UE is preferable.
[Show abstract][Hide abstract] ABSTRACT: In this article we consider the problem of estimating the coefficient vector of a classical regression model when it is apriori suspected that the parameters vector may belong to a subspace. Two estimators; namely the positive-part of Stein-type estimator and the improved preliminary test estimator are proposed and it is demonstrated analytically as well as numerically that the proposed estimators dominate the usual Stein-type and pretest estimators respectively. The proposed estimators are also compared in terms of risks with that of the unrestricted estimator and we find that the positive-part of Stein-type estimator uniformly dominates the unrestricted estimator while the improved preliminary test estimator dominates the unrestricted estimator in a wider range than that of the usual pretest estimator.
Communication in Statistics- Simulation and Computation 01/2003; 32(3):747-769. DOI:10.1081/SAC-120017860 · 0.33 Impact Factor