A Generalized Extreme Studentized Residual Multiple-Outlier-Detection Procedure in Linear Regression

This article is concerned with procedures for detecting multiple y outhers in linear regression. A generalized extreme studentized residual (GESR) procedure, which controls type I error rate, is developed. An approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n ≤ 25 are tabulated. The performance of this procedure is compared with others by Monte Carlo techniques and found to be superior. The procedure. however, fails in detecting y outliers that are on high-leverage cases. For this. a two-phase procedure is suggested. In phase 1, a set of suspect observations is identified by GESR and one of the diagnostics applied sequentially. In phase 2, a backward testing is conducted using the GESR procedure to see which of the suspect cases are outlicrs. Several examples are analyzed.