Estimation and Inference in Regression Models with Asymmetric Error Distributions: a Comparison of Lav and Ls Procedures
نویسنده
چکیده
Introduction and Summary The use of regression analysis relies on the choice of a criterion in order to estimate the coefficients of the explanatory variables. Traditionally, the least squares (LS) criterion has been the method of choice. However, the least absolute value (LAV) criterion provides an alternative. LAV regression coefficients are chosen to minimize the sum of the absolute values of the residuals. By minimizing sums of absolute values rather than sums of squares, the effect of outliers on the coefficient estimates is diminished. In most previous studies comparing the performance of LAV and LS estimation, the distributions examined have been symmetric. “Fat-tailed” distributions that introduce outliers have been used, but these have typically been symmetric fat-tailed distributions (Laplace, Cauchy, etc). This paper examines the performance of LAV and LS coefficient estimators when the regression disturbances come from asymmetric distributions. Also, hypothesis tests for coefficient significance are examined. For the LAV regression, the tests compared include the likelihood ratio (LR) test and the Lagrange multiplier (LM) test suggested by Koenker and Bassett (1982) as well as a bootstrap test. The tests are compared in terms of both observed significance level and empirical power. The LAV tests are also compared with the traditional t-test for LS regression.
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