Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection

Abstract

An estimator $\hat{\beta}$ of $\beta$ is accurate with accuracy $A$ and confidence $\gamma, 0 < \gamma < 1,$ if $P(\hat{\beta} - \beta \in A) \geq \gamma$ for all $\beta.$ Given a sequence $Y_1, Y_2, \cdots$ of independent vector-valued homoscedastic normally-distributed random variables generated via the general linear model $Y_i = X_i\beta + \varepsilon,$ the $k$-dimensional parameter $\beta$ is accurately estimated using a sequential version of the maximum probability estimator developed by L. Weiss and J. Wolfowitz. The procedure given also generalizes C. Stein's fixed-width confidence sets to several dimensions.