A Multistage Procedure for Detecting Several Outliers in Linear Regression

Abstract

A new statistic, F_k , 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 F_k 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:

• Residuals
• Studentized residuals
• Mutliple regression
• Multiple outliers
• Stagewise tests