The problem of simultaneous estimation of the regression parameters in a multiple regression model with measurement errors is considered when it is suspected that the regression parameter vector may be the null-vector with some degree of uncertainty. In this regard, we propose two sets of four estimators, namely, (i) the unrestricted estimator, (ii) the preliminary test estimator, (iii) the Stein-type estimator and (iv) the postive-rule Stein-type estimator. In an asymptotic setup, properties of these estimators are studied based on asymptotic distributional bias, MSE matrices, and risks under a quadratic loss function. In addition to the asymptotic dominance of the Stein-type estimators, the paper contains discussion of dominating confidence sets based on the Stein-type estimation. Asymptotic analysis is considered based on a sequence of local alternatives to obtain the desired results.

This article addresses the problem of heterogeneity among various studies to be combined in a meta-analysis. We adopt quasi-empirical Bayes methodology to predict the odds ratios for each study. As a result, the predicted odds ratios are pulled toward the estimated common odds ratio of the various studies under consideration. With strong heterogeneity among the studies, we jointly consider the display of the 95% CIs of the ORs and a Dixon's test (1950) for "outliers" to exclude the "extreme" estimated ORs. We demonstrate the effectiveness of our methodology based on the data analyzed by Thompson and Pocock (1987) demonstrating the power of the new approach to meta-analysis to find statistical agreement in what looks like great disagreement via a chi-squared test. We believe our technique (i.e., minimum mean-square sense) will go a long way toward increasing the trustworthiness of meta-analysis.