 
Summary: A normality test for the errors of the linear
model
Miguel A. Arcones
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902.
Email:arcones@math.binghamton.edu
January 27, 2008
Abstract
We present a normality test for the errors of the linear regression model based on the
normality test in Epps and Pulley (1983). We prove that the presented test is consistent
against any alternative. We show that the test statistic under the null hypothesis is
asympotically equivalent to a degenerate Vstatistic. We also consider the asymptotic
distribution of the test under contiguous alternatives.
1 Introduction
Many of the statistical methods in linear regression assume that the residuals have a normal
distribution. In this paper, we study a normality test for the residuals of a linear regression
model. Many authors have studied normality tests for (independent identically distributed)
i.i.d. observations. Reviews of normality tests are Henze (2002) and Mecklin and Mundfrom
(2004). Classical normality tests are the ones by Shapiro and Wilk (1965, 1968) and Epps
and Pulley (1983). Several authors have considered tests of normality for the linear regression
model. Jureckov´a, Picek, and Sen (2003) and Sen, Jureckov´a, and Picek (2003) considered a
