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...

We continue an investigation into resource-bounded Kolmogorov complexity [ABK06], which highlights the close connections between circuit complexity and Levin’s time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding Kolmogorov complexity. The Kolmogorov measures that have been introd...

While Kolmogorov complexity is the accepted absolute measure of information content of an individual nite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing the information in the data, for example, a nite set where the data sample typically came from. The statistical theory based on such relations between individ...

This paper examines the channel holding time of public cellular telephony systems. This is the time that the Mobile Station (MS) remains in the same cell, a fraction of the call holding time. The study is based on actual data taken from a working system. The probability distribution that fits the empirical sample best when applying the Kolmogorov-Smirnov test is a mixture of lognormals. Combina...

This paper focuses on a general setup for obtaining sample size lower bounds for learning concept classes under fixed distribution laws in an extended PAC learning framework. These bounds do not depend on the running time of learning procedures and are information-theoretic in nature. They are based on incompressibility methods drawn from Kolmogorov Complexity and Algorithmic Probability theori...

We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces (X, d, μ1) and (X, d, μ2), we are interested in the problem of determining from finite data whether or not μ1 is μ2. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogo...

Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1, X2, . . . , Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased ...