Related papers: Testing to distinguish measures on metric spaces
In this article a new family of tests is proposed for the comparison problem of the equality of distribution of two-sample under right censoring scheme. The tests are based on energy distance and kernels mean embedding, are calibrated by…
We consider the problem of statistical inference for the S distribution and introduce new minimum distance estimators for the four parameters of the S distribution using Kolmogorov-Smirnov, Cramer-von Mises and related distance metrics.…
Let $(X\_1,\ldots,X\_n)$ be a $d$-dimensional i.i.d sample from a distribution with density $f$. The problem of detection of a two-component mixture is considered. Our aim is to decide whether $f$ is the density of a standard Gaussian…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Color based re-identification methods usually rely on a distance function to measure the similarity between individuals. In this paper we study the behavior of several histogram distance measures in different color spaces. We wonder whether…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special…
We investigate the statistics of the cosmic microwave background using the Kolmogorov-Smirnov test. We show that, when we correctly de-correlate the data, the partition function of the Kolmogorov stochasticity parameter is compatible with…
We consider a family of measures on a $q$-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
Following the line of classification-based two-sample testing, tests based on the Random Forest classifier are proposed. The developed tests are easy to use, require almost no tuning, and are applicable for any distribution on…
Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…
Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be…
We examine the integrated squared difference, also known as the L2 distance (L2D), between two probability densities. Such a distance metric allows for comparison of differences between pairs of distributions or changes in a distribution…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
Information collection is a fundamental problem in big data, where the size of sampling sets plays a very important role. This work considers the information collection process by taking message importance into account. Similar to…