Multiple Regression and Estimation of the Mean of a Multivariate Normal Distribution

摘要

Two problems are presented in this study: estimation of the mean vector of a multivariate normal random variable, and estimating the regression function in the case of one predictand and at least three predictors. Estimators are given which have strictly lower risks than the corresponding maximum likelihood estimators for the following three problems: (a) estimation of the regression function; (b) estimation of the regression coefficients; and (c) estimation of the mean of the predict and when the means of the predictor variables are known. In each of the problems it is assumed that there are at least three predictor variables. A summary of previously known results for these three problems is given. The report concludes with some elementary modifications of the estimators computed earlier in the report. The author remarks that these modified estimators will frequently be of practical use.