Journal
MATHEMATICAL METHODS OF STATISTICS
Volume 26, Issue 3, Pages 212-225Publisher
PLEIADES PUBLISHING INC
DOI: 10.3103/S1066530717030048
Keywords
Dirichlet process; goodness-of-fit tests; Kolmogorov distance; two-sample problem
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Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC)
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In this paper, a Bayesian nonparametric approach to the two-sample problem is proposed. Given two samples X = X-1, ..., X-m1 ((i.i.d.) under tilde) F and Y = Y-1, ..., Y-m2 ((i.i.d.) under tilde) G, with F and G being unknown continuous cumulative distribution functions, we wish to test the null hypothesis H-0 : F = G. The method is based on computing the Kolmogorov distance between two posterior Dirichlet processes and comparing the results with a reference distance. The parameters of the Dirichlet processes are selected so that any discrepancy between the posterior distance and the reference distance is related to the difference between the two samples. Relevant theoretical properties of the procedure are also developed. Through simulated examples, the approach is compared to the frequentist Kolmogorov-Smirnov test and a Bayesian nonparametric test in which it demonstrates excellent performance.
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