Advances and Applications in Statistics
Volume 17, Issue 2, Pages 161 - 173
(August 2010)
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ON THE USE OF THE KULLBACK-LEIBLER DISTANCE FOR THE TWO-SAMPLE PROBLEM WITH MIXED DATA
M. D. Jiménez-Gamero and M. V. Alba-Fernández
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Abstract: A widely used distribution to model mixed data is the conditional Gaussian model. In this paper, we study the problem of testing the homogeneity of two conditional Gaussian populations. With this aim, we consider as test statistic a sample version of the Kullback-Leibler distance between these populations. It is shown that the test that rejects the null hypothesis for large values of this test statistic is consistent against fixed alternatives. In order to estimate the null distribution of the test statistic we consider two approximations: the asymptotic null distribution and a parametric bootstrap estimator. It is shown that both approximations are asymptotically equivalent. Their finite sample performance are studied by simulation. |
Keywords and phrases: conditional Gaussian distribution, two-sample problem, Kullback- Leibler distance, consistent test, bootstrap. |
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