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Two-sample smooth tests for the equality of distributions
- Source :
- Bernoulli, vol 23, iss 2, Bernoulli 23, no. 2 (2017), 951-989
- Publication Year :
- 2017
- Publisher :
- eScholarship, University of California, 2017.
-
Abstract
- This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-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.<br />Comment: 40 pages, 3 figures
- Subjects :
- Statistics and Probability
FOS: Computer and information sciences
Multivariate statistics
goodness-of-fit
Omnibus test
Statistics & Probability
Neyman’s smooth test
Mathematics - Statistics Theory
Statistics Theory (math.ST)
01 natural sciences
Methodology (stat.ME)
010104 statistics & probability
two-sample problem
multiplier bootstrap
Dimension (vector space)
Goodness of fit
0502 economics and business
FOS: Mathematics
Neyman's smooth test
Applied mathematics
Statistics::Methodology
Econometrics
0101 mathematics
Projection (set theory)
Statistics - Methodology
050205 econometrics
Mathematics
high-frequency alternations
05 social sciences
Null (mathematics)
Statistics
16. Peace & justice
Critical value
Sample size determination
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Bernoulli, vol 23, iss 2, Bernoulli 23, no. 2 (2017), 951-989
- Accession number :
- edsair.doi.dedup.....7f04883d275059ab6bb38bc044d3f3a4