Fast calibrations of the forward search for testing multiple outliers in regression

Abstract

The paper considers the problem of testing for multiple outliers in a regression model and provides fast approximations to the null distribution of the minimum deletion residual used as a test statistic. Since direct simulation of each combination of number of observations and number of parameters is too time consuming, methods using simple normal samples are described for approximating the pointwise distribution of the test statistic. One approximation is based on adjustments to the results of simple simulations. The other uses properties of order statistics from folded t distributions to move outside the significance levels available by simulation. Analyses of data with beta errors and of transformed data on survival times demonstrate the usefulness in graphical methods of the inclusion of our bounds.