A data-driven test for dispersive ordering (Q1304057)

Two distribution functions with unknown Lebesgue densities \(f\) and \(g\) are compared through \(\Delta = \int f_n^2 - \int g_m^2\), where \(f_n\) and \(g_m\) are appropriate kernel estimators of \(f\) and \(g\). The bandwidths are chosen via cross-validation. The paper provides the limit distribution of \(\Delta\) under the hypothesis \(f = g\). This result may be viewed as the two-sample analogue of \textit{T.-J. Wu}, Ann. Stat. 23, No. 5, 1474-1495 (1995; Zbl 0843.62036).