A bootstrap approach to hypothesis testing in least absolute value regression

Abstract

This study compares three alternative procedures for testing the significance of coefficients in least absolute value (LAV) regression, in the context of small samples. The three tests considered are: the likelihood ratio test using an estimator of the nuisance parameter proposed by McKean and Schrader (Comm. Statist. Simulation Comput. 13 (1984)), the Lagrange multiplier test, and a bootstrap test in which critical values of the test statistic are obtained by resampling. Comparisons among the tests are made by considering both observed significance levels and power. The bootstrap test used in this study performs well, compared to the other two tests. This result is in contrast to results, involving a somewhat different use of the bootstrap technique, obtained by Dielman and Pfaffenberger (Comput. Statist. Data Anal. 14 (1992)), and suggests that the use of the technique proposed in this paper has strong potential for applicability in hypothesis testing for LAV regression.