Checking the adequacy of the multivariate semiparametric location shift model |
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| Authors: | N Henze B Klar L X Zhu |
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| Institution: | a Institute of Mathematical Stochastics, University of Karlsruhe, Germany;b Department of Statistics and Actuarial Sciences, University of Hong Kong, Hong Kong, China;c East China Normal University, China |
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| Abstract: | Let X,X1,…,Xm,…, Y,Y1,…,Yn,… be independent d-dimensional random vectors, where the Xj are i.i.d. copies of X, and the Yk are i.i.d. copies of Y. We study a class of consistent tests for the hypothesis that Y has the same distribution as X+μ for some unspecified
. The test statistic L is a weighted integral of the squared modulus of the difference of the empirical characteristic functions of
and Y1,…,Yn, where
is an estimator of μ. An alternative representation of L is given in terms of an L2-distance between two nonparametric density estimators. The finite-sample and asymptotic null distribution of L is independent of μ. Carried out as a bootstrap or permutation procedure, the test is asymptotically of a given size, irrespective of the unknown underlying distribution. A large-scale simulation study shows that the permutation procedure performs better than the bootstrap. |
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| Keywords: | Goodness-of-fit test Multivariate location model Empirical characteristic function Permutational principle Bootstrap |
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