We propose a way to construct consistent generalizations of the Cram er-von Mises test on the line, and the Watson U 2 n test on the circle, based on classes of partitions invariant under various group actions. The framework developed extends our earlier work generalizing the Kolmogorov-Smirnov and Kuiper goodness-oft tests, and provides a conceptually unifying description. Many goodness-oft te...

A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This method is very fast and thus well suited for on-line applications. It is robust to noise and its performances in terms of precision are excellent for shift times ...

In this note we discuss in general how to test the implementation code of statistical tests, and then we treat in detail the case of the Kolmogorov-Smirnov test. It will be shown that some “obvious” expected properties, like the flatness distributions of p-values from repeating drawings from the same parent distribution, are not indeed reproduced even in absence of bugs in the code, due to eith...

An important problem in statistics is to obtain information about the form of the population from which the sample is drawn. Goodness of fit test is employed to determine how well the observed sample data "fits" some proposed model. The standard goodness of fit statistics are inappropriate when the parameters of the hypothesized distribution are estimated from the data used for the test. In thi...

In this chapter, we consider some chi-square-type goodness-of-fit tests for right AQ1 censored samples, viz. the Nikulin–Rao–Robson (NRR) test and generalized Pearson–Fisher (GPF) test. We compare these tests in terms of power in the case of testing composite hypotheses by randomly censored and Type II censored samples. Various grouping methods are considered, including equifrequent grouping, g...

A theme of recent side-channel research has been the quest for distinguishers which remain e ective even when few assumptions can be made about the underlying distribution of the measured leakage traces. The Kolmogorov-Smirnov (KS) test is a well known non-parametric method for distinguishing between distributions, and, as such, a perfect candidate and an interesting competitor to the (already ...

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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. ...

We introduce a nonparametric test intended for large-scale simultaneous inference in situations where the utility of distribution-free tests is limited because of their discrete nature. Such situations are frequently dealt with in microarray analysis where the number of tests is much larger than the sample size. The proposed test statistic is based on a certain distance between the distribution...