Distribution Theory and Simulations for Tests of Outliers in Regression

This article provides distributional results for testing multiple outliers in regression. Because direct simulation of each combination of number of observations and number of parameters is too time consuming, three straightforward methods using truncated simple samples are described for approximating the pointwise distribution of the test statistic. Scaling factors are found to adjust for the number of parameters. The same simulations also provide a powerful method of calibrating pointwise inferences for simultaneous tests for an unknown number of outliers. Analysis of data on fidelity cards reveals an unexpected group of outliers.