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Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…
We analyze safety problems of complex systems using the methods of mathematical statistics for testing the output variables of a code simulating the operation of the system under consideration when the input variables are uncertain. We have…
There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…
In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is $(X_{1}, X_{2})$ but we observe only $Y_1 = \min\{X_{1},X_{2}\}$ and $Y_2 = \max\{X_{1},X_{2}\}$, i.e., the…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
Ordinal categorical data are widely collected in psychology, education, and other social sciences, appearing commonly in questionnaires, assessments, and surveys. Latent class models provide a flexible framework for uncovering unobserved…
We analyze the ordinal structure of long-range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal…
While supporting the execution of business processes, information systems record event logs. Conformance checking relies on these logs to analyze whether the recorded behavior of a process conforms to the behavior of a normative…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
A common method for deriving non-parametric tests is to reformulate a parametric test in terms of sample ranks. Despite being distribution free (even in finite samples), the resulting tests often display remarkable asymptotic power…
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.
This paper focuses on a data-rich environment where the data set has a very large cross-sectional dimension, is likely to exhibit local dependence, and yet is hard to determine the dependence ordering. Such a situation arises, for example,…
We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…