Empirical results on distance of two-dimensional samples

Abstract

The distance of two-dimensional samples is studied. The distance of two samples is based on the optimal matching method. Simulation results are obtained when the samples are drawn from normal and uniform distributions.

On the asymptotics of Ajtai-Komlós-Tusnády statistics

“…The first application of the AKT theorem was in bin packing [5]. A numerical investigation of the distribution of the statistic was given in [8]. Matchings on the Euclidean ball were investigated in [3].…”

“…, thus the distribution of R(X) is standard exponential and the distribution of exp(−R(X)) is again uniform in (0, 1). So we can test the hypothesis that the distribution of the 67 dimensional Wasserstein statistics belongs to the three parameter family (8) testing the uniformity of this statistics. Of course we can not use the original Kolmogorov cut-points because we use estimated parameters, we have to calibrate the cut-points by random sample.…”