Related papers: A unified framework for multivariate two-sample an…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
This paper is devoted to multi-dimensional inverse problems. In this setting, we address a goodness-of-fit testing problem. We investigate the separation rates associated to different kinds of smoothness assumptions and different degrees of…
Goodness-of-fit tests based on the Euclidean distance often outperform chi-square and other classical tests (including the standard exact tests) by at least an order of magnitude when the model being tested for goodness-of-fit is a discrete…
We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance…
Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…
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…
We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
In recent years, Bayesian nonparametric statistics has gathered extraordinary attention. Nonetheless, a relatively little amount of work has been expended on Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian…
We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
We discuss a goodness-of-fit method which tests the compatibility between statistically independent data sets. The method gives sensible results even in cases where the chi^2-minima of the individual data sets are very low or when several…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…
Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…