A Multistage Procedure for Detecting Several Outliers in Linear Regression

Abstract

Abstract A new statistic, Fk , is proposed for detecting multiple outliers in linear regression. This statistic is incorporated into the following multistage procedure: Initially, a subset of k observations is selected to be tested. If Fk is found to be significant, the most extreme observation in the subset as determined by the largest studentized residual is deleted and the test repeated for the (k – 1) observations in the subset using the remaining sample. The procedure is stopped when a test fails to reject the no-outlier hypothesis. A Monte Carlo study is used to evaluate the performance of this procedure. KEY WORDS: ResidualsStudentized residualsMutliple regressionMultiple outliersStagewise tests