Heuristic Approach to the Kolmogorov-Smirnov Theorems

摘要: Asymptotic theorems on the difference between (empirical) distribution function calculated from a sample and true governing sampling process are well known. Simple proofs of an elementary nature have been obtained for basic Komogorov Smirnov by Feller, but even these conceal to some extent, in their emphasis methodology, naturalness results (qualitatively at least), mutual relations. Feller suggested that author publish his own approach (which had also used Kac), which does not disadvantages, although rather deep analysis would be necessary its rigorous justification. The is therefore presented (at one critical point) as heuristic reasoning leads investigations this kind, though easiest may use entirely different methods. No calculations required obtain qualitative results, existence limiting distributions large samples various measures discrepancy empirical functions. numerical evaluation requires certain concerning Brownian movement stochastic relation other Gaussian processes will derived Appendix.