On the Bounds for Diagonal and Off-Diagonal Elements of the Hat Matrix in the Linear Regression Model

Abstract

In the least squares analysis, an appropriate criterion to detect potentially influential observations, either individually or jointly, deals with the values of corresponding Hat matrix elements. Hence, some conditions for which these elements give the extreme values are interesting in the model sensitivity analysis. In this article, we find a new and sharper lower bound for off-diagonal elements of the Hat matrix in the intercept model, which is shorter than those for the no-intercept model. We give necessary and sufficient conditions on the space of design matrix, under which the corresponding Hat matrix elements get desired extreme values.