JSM 2005 Online Program

Abstract #304328

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Activity Number:	36
Type:	Contributed
Date/Time:	Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #304328
Title:	On the Llink between Smooth and EDF Tests for Goodness-of-fit
Author(s):	Olivier Thas*+ and John Rayner
Companies:	Ghent University and University of Wollongong
Address:	Coupure Links 653, Gent, 9000, Belgium
Keywords:	Cramer-von Mises ; orthonormal polynomials
Abstract:	We consider the one-sample goodness-of-fit problem. A well-known class of tests are the EDF tests, which are based on the empirical distribution function (EDF). This class includes the Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises tests. Here, we focus on a large family of weighted Cramér-von Mises tests. Another type of tests are the Neyman smooth tests, which are basically score tests in a large class of alternatives in which the hypothesized distribution is embedded. Although both types of tests were originally developed independently, Durbin and Knot (1972) have shown that, when testing for uniformity, the components of a smooth test statistic appear exactly in the principal component representation of some EDF test statistic. In this paper, we first show that this link holds true for a larger class of EDF and smooth tests. Once this relation is established, some new EDF tests emerge. In particular, new EDF tests for the normal and exponential distribution are discussed in detail.

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