A Bayesian Motivated Two-Sample Test Based on Kernel Density Estimates. Academic Article uri icon


  • A new nonparametric test of equality of two densities is investigated. The test statistic is an average of log-Bayes factors, each of which is constructed from a kernel density estimate. Prior densities for the bandwidths of the kernel estimates are required, and it is shown how to choose priors so that the log-Bayes factors can be calculated exactly. Critical values of the test statistic are determined by a permutation distribution, conditional on the data. An attractive property of the methodology is that a critical value of 0 leads to a test for which both type I and II error probabilities tend to 0 as sample sizes tend to . Existing results on Kullback-Leibler loss of kernel estimates are crucial to obtaining these asymptotic results, and also imply that the proposed test works best with heavy-tailed kernels. Finite sample characteristics of the test are studied via simulation, and extensions to multivariate data are straightforward, as illustrated by an application to bivariate connectionist data.

published proceedings

  • Entropy (Basel)

altmetric score

  • 0.5

author list (cited authors)

  • Merchant, N., & Hart, J. D.

citation count

  • 0

complete list of authors

  • Merchant, Naveed||Hart, Jeffrey D

publication date

  • January 2022