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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Two-sample smooth tests for the equality of distributions
AU - Zhou, Wen-Xin
AU - Zheng, Chao
AU - Zhang, Zhen
PY - 2017/2/4
Y1 - 2017/2/4
N2 - This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov–Smirnov and Cramér–von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman’s smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components.
AB - This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov–Smirnov and Cramér–von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman’s smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components.
KW - goodness-of-fit
KW - high-frequency alternations
KW - multiplier bootstrap
KW - Neyman’s smooth test
KW - two-sample problem
U2 - 10.3150/15-BEJ766
DO - 10.3150/15-BEJ766
M3 - Journal article
VL - 23
SP - 951
EP - 989
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 2
ER -