TY - JOUR

T1 - Two-sample Kolmogorov-Smirnov test using a Bayesian nonparametric approach

AU - Al-Labadi, L.

AU - Zarepour, M.

N1 - Funding Information:
8. ACKNOWLEDGMENTS We would like to thank the editors and an anonymous referee for their careful review of the paper and their extremely helpful comments. Research of the second author is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
Publisher Copyright:
© 2017, Allerton Press, Inc.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - In this paper, a Bayesian nonparametric approach to the two-sample problem is proposed. Given two samples X=X1,…,Xm1~i.i.d.F and Y=Y1,…,Ym2~i.i.d.G, with F and G being unknown continuous cumulative distribution functions, we wish to test the null hypothesis H0: 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.

AB - In this paper, a Bayesian nonparametric approach to the two-sample problem is proposed. Given two samples X=X1,…,Xm1~i.i.d.F and Y=Y1,…,Ym2~i.i.d.G, with F and G being unknown continuous cumulative distribution functions, we wish to test the null hypothesis H0: 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.

KW - Dirichlet process

KW - Kolmogorov distance

KW - goodness-of-fit tests

KW - two-sample problem

UR - http://www.scopus.com/inward/record.url?scp=85029805493&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029805493&partnerID=8YFLogxK

U2 - 10.3103/S1066530717030048

DO - 10.3103/S1066530717030048

M3 - Article

AN - SCOPUS:85029805493

SN - 1066-5307

VL - 26

SP - 212

EP - 225

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

IS - 3

ER -