A homogeneity test based on empirical characteristic functions (Q1861608)

A two-sample test for homogeneity is described which is based on the statistics \[ D_T=\sqrt{\int_R|c_n(t)-c_m(t)|^2dt}, \] where \(c_n\) and \(c_m\) are the empirical characteristic functions of the first and the second samples. A method of numerical integration is proposed for the calculation of \(D_T\) by data. A bootstrap procedure is used for the estimation of the critical level of the test. Consistency of the test is demonstrated and its asymptotic power is evaluated. Results of simulations for the normal distribution are presented. It is shown that the described test can be more powerful than the Kolmogorov-Smirnov test on Lehmann type nonparametric alternatives.