Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10524486 | Journal of Multivariate Analysis | 2005 | 19 Pages |
Abstract
Let X,X1,â¦,Xm,â¦, Y,Y1,â¦,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 μâRd. The test statistic L is a weighted integral of the squared modulus of the difference of the empirical characteristic functions of X1+μÌ,â¦,Xm+Î¼Ì and Y1,â¦,Yn, where Î¼Ì 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
N. Henze, B. Klar, L.X. Zhu,