Two-sample Bayesian nonparametric goodness-of-fit test
| Autor: | Labadi, Luai Al, Masuadi, Emad, Zarepour, Mahmoud |
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| Rok vydání: | 2014 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In recent years, Bayesian nonparametric statistics has gathered extraordinary attention. Nonetheless, a relatively little amount of work has been expended on Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian nonparametric approach to the two-sample problem is established. Precisely, given two samples $\mathbf{X}=X_1,\ldots,X_{m_1}$ $\overset {i.i.d.} \sim F$ and $\mathbf{Y}=Y_1,\ldots,Y_{m_2} \overset {i.i.d.} \sim G$, with $F$ and $G$ being unknown continuous cumulative distribution functions, we wish to test the null hypothesis $\mathcal{H}_0:~F=G$. The method is based on the Kolmogorov distance and approximate samples from the Dirichlet process centered at the standard normal distribution and a concentration parameter 1. It is demonstrated that the proposed test is robust with respect to any prior specification of the Dirichlet process. A power comparison with several well-known tests is incorporated. In particular, the proposed test dominates the standard Kolmogorov-Smirnov test in all the cases examined in the paper. Comment: 25 pages, 8 figures |
| Databáze: | arXiv |
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