Testing for outliers and influential observations in multiple regression using restricted least squares

In this paper, the prior information is in the form of linear restrictions on the parameters. Test statistics and diagnostics are developed to test for outliers and to detect influential observations when the residuals are analyzed, after these residuals have been computed using the restrictions on the parameters. The distributional results for both single and multiple outliers and influential observations are given The distributions of the test statistics and diagnostics are complicated non-central distributions. Under certain assumptions (for example exact restrictions) the distributions simplify to central distributions. Comparisons can then be made with traditional test statistics and diagnostics. The results are demonstrated using a simulated data set and also two known practical examples in the literature. The data used are those of Belsley, Kuh and Welsch (1980) and Chatterjee and Hadi (1986).