Facultade de Fisioterapia

An approximation to the null distribution of a class of Cramer-von Mises statistics

Jiménez Gamero, María Dolores; Alba Fernández, M.V.; Jodrá, P.; Baranco Chamorro, I.
Abstract:
A class of goodness-of-fit tests of the Cramer-von Mises type is considered. More specifically, the test statistic of each test is an L-2-norm of the difference between the empirical characteristic function associated with a random sample and a parametric estimator of the characteristic function of the population in the null hypothesis. The null distribution of these statistics is unknown and we study a way of estimating it, which is based on approximating the asymptotic null distribution. The asymptotic null distribution is a linear combination of independent chi-squared variates, where the weights are the eigenvalues of certain operator. The calculation of these eigenvalues is, in most cases, a very difficult task. In order to bypass this computation we approximate the test statistic. The asymptotic null distribution of the approximation is again a linear combination of chi-squared variates, but now the weights can be easily approximated. A simulation study is carried out to examine the accuracy of the proposed approximation for finite sample sizes. Although we center our attention on the aforementioned class, the methodology exposed can be applied for approximating the null distribution of other Cramer-von Mises type test statistics. (C) 2014 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Year:
2015
Type of Publication:
Article
Keywords:
Goodness-of-fit; Empirical characteristic function; Null distribution; Taylor approximation
Journal:
Mathematics and Computers in Simulation
Volume:
118
Pages:
258-272
Month:
December
DOI:
http://dx.doi.org/10.1016/j.matcom.2014.11.011
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