On Some Results and Problems in Connection with Statistics of the Kolmogorov Smirnov Type
Hungarian Academy of Sciences Budapest Hungary
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Since Kolmogorov and Smirnov established their limiting distribution theorems concerning maximal deviations between empirical and theoretical distributions, an increasing amount of scientific work has been done by statisticians in this field. Practical importance and theoretical interest give the motivation. Researchers have worked on distribution laws, power considerations and the limiting process in the last five years with considerable results. The present paper will consider only a few results, those nearest to the authors work and interest of the past few years. The first part, Section 2. concerns the case when the parent distribution is noncontinuous, the third and fourth sections consider the one and two sample problem, in the fifth section an analogous question for a density function due to Revesz is discussed, while in the last section the two dimensional problem is considered.