Exact Bahadur Efficiencies for the Kolmogorov-Smirnov and Kuiper One- and Two-Sample Statistics

Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics.

We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2012) concerning exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving correspondi...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Sure Invariance Principle for Multivariate Kolmogorov - Smirnov Statistics

A fast algorithm for two-dimensional Kolmogorov-Smirnov two sample tests

By using the brute force algorithm, the application of the two-dimensional two-sample Kolmogorov–Smirnov test can be prohibitively computationally expensive. Thus a fast algorithm for computing the two-sample Kolmogorov–Smirnov test statistic is proposed to alleviate this problem. The newly proposed algorithm is O(n) times more efficient than the brute force algorithm, where n is the sum of the...

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov-Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the KolmogorovSmirnov two sample statistic. ...