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A TEST FOR SPHERICITY OF ERRORS IN LINEAR MODELS
作者姓名:WANG  Songgui
作者单位:WANG Songgui(Institute of Statistics,Beijing Polytechnic University,Beijing 100022,China)(Institute of Applied of Mathematics,Academia Sinica,Beijing 100080,China)YANG Zhenhai(Institute of Statistics,Beijing Polytechnic University,Beijing 100022
摘    要:1.IntroductionConsideragenerallinearmodelwhereyisannx1vectorofobservations,Xisannxpdesignmatrixwithrankp,Pisapx1vectorofparameters,e~(el,',e.)'isavectorofrandomerrors.Inthestatisticalliterature,itisoftenassumedthatei,i~1,')ushavetheindependentnormaldi…


A TEST FOR SPHERICITY OF ERRORS IN LINEAR MODELS
WANG Songgui.A TEST FOR SPHERICITY OF ERRORS IN LINEAR MODELS[J].Journal of Systems Science and Complexity,1997(3).
Authors:WANG Songgui
Abstract:For a general linear model, spherical distributions are often considered whenerrors do not have normal distribution. Several authors1-3] studied the least squaresand James-Stein estimations for a linear model whose errors follow multivariate t or moregeneral spherical distributions. In this paper the test problem for sphericity of errors isconsidered. We propose an exact test for the sphericity by using the conditional probabilityintegral transformation and another transformation. As an important special case, thecorresponding test statistics for multivariate t distribution are obtained.
Keywords:Spherical distribution  multivariate t-distribution  conditional probability integral transformation  Pearson's product test  multivariate Cauchy distribution  
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