Limiting Distributions of Kolmogorov-Smirnov Type Statistics Under the Alternative

On Some Results and Problems in Connection with Statistics of the Kolmogorov-smirnov Type

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 pro...

Assessment of nonlinear dynamic models by Kolmogorov-Smirnov statistics

Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov–Smirnov statistics. The technique is based on the generation of dis...

Approximations for weighted Kolmogorov-Smirnov distributions via boundary crossing probabilities

A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of themaximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an n-dimensional Ga...

Sure Invariance Principle for Multivariate Kolmogorov - Smirnov Statistics

Small Improvement to the Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with nea...