Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates

Test statistics are proposed for testing equality of two p-variate probability density functions. The statistics are based on the integrated square distance between two kernel-based density estimates and are two-sample versions of the statistic studied by Hall (1984, J. Multivariate Anal. 14 1-16). Particular emphasis is laid on the case where the two bandwidths are fixed and equal. Asymptotic distributional results and power calculations are supplemented by an empirical study based on univariate examples.