An adaptive test of a subset of regression coefficients using permutations of residuals

Abstract

An adaptive test is proposed that has greater power than the traditional F-test in linear models that have non-normal errors. The proposed test uses the studentized deleted residuals that are calculated from the reduced model to estimate the appropriate weights for the observations. These weights are then used in a weighted least-squares model to compute the test statistic. Unlike other adaptive tests, this test uses a method based on the permutation of ordinary residuals to estimate the p-value, which has the advantage of not disturbing the relationships among predictor variables. The adaptive test maintains its level of significance for a wide variety of sample sizes and error distributions. The power of the adaptive test approximates the power of the traditional F-test for models having normal errors and exceeds the power of the traditional test for most of the models having non-normal errors.