Nonnormal Regression.I. Skew Distributions

Abstract

In a linear regression model of the typey¼ Xþe, it is oftenassumed that the random erroreis normally distributed. Innumerous situations, e.g., whenymeasures life times or reac-tion times,etypically has a skew distribution. We considertwo important families of skew distributions, (a) Weibull withsupport IR:ð0,1Þon the real line, and (b) generalised logisticwit hsupport IR:ð 1,1Þ. Since the maximum likelihoodestimators are intractable in these situations, we derivemodified likelihood estimators which have explicit algebraicforms and are, therefore, easy to compute. We show that theseestimators are remarkably efficient, and robust. We develophypothesis testing procedures and give a real life example