Some applications of the Gnedenko–Korolyuk method to empirical distributions
E. O. Lutsenko, O. V. Marinich, Ivan K Matsak · Theory of Probability and Mathematical Statistics · 2009
A new proof of the Kolmogorov theorem on the asymptotic behavior of the deviation between a theoretical and an empirical distribution function is presented. We use the Gnedenko–Korolyuk approach based on some combinatorial properties of the merged sample constructed from two other independent samples. Some statistical applications of the Gnedenko–Korolyuk theorem are discussed.