Related papers: A Robust Test for Elliptical Symmetry
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
While training fair machine learning models has been studied extensively in recent years, most developed methods rely on the assumption that the training and test data have similar distributions. In the presence of distribution shifts, fair…
Universal hypothesis testing refers to the problem of deciding whether samples come from a nominal distribution or an unknown distribution that is different from the nominal distribution. Hoeffding's test, whose test statistic is equivalent…
A fundamental assumption underling any Hypothesis Testing (HT) problem is that the available data follow the parametric model assumed to derive the test statistic. Nevertheless, a perfect match between the true and the assumed data models…
Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To…
We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for…
We introduce two new tools to assess the validity of statistical distributions. These tools are based on components derived from a new statistical quantity, the $comparison$ $curve$. The first tool is a graphical representation of these…
This paper proposes a goodness of fit test for the generalized Pareto distribution (GPD). Firstly, we provide two characterizations of GPD based on Stein's identity and dynamic survival extropy. These characterizations are used to test GPD…
We study distributed goodness-of-fit testing for discrete distribution under bandwidth and differential privacy constraints. Information constraint distributed goodness-of-fit testing is a problem that has received considerable attention…
We propose a two-sample test for large-dimensional covariance matrices in generalized elliptical models. The test statistic is based on a U-statistic estimator of the squared Frobenius norm of the difference between the two population…
We present the first method for assessing the relevance of a model-based clustering result in a general framework. Standard validation criteria, like the adjusted Rand index, rely on external labels to assess partition accuracy;…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
Temperature data, like many other measurements in quantitative fields, are usually modeled using a normal distribution. However, some distributions can offer a better fit while avoiding underestimation of tail event probabilities. To this…
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…
Suppose we want to estimate a total effect with covariate adjustment in a linear structural equation model. We have a causal graph to decide what covariates to adjust for, but are uncertain about the graph. Here, we propose a testing…
We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…
In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian…
Given an i.i.d. sample drawn from a density $f$, we propose to test that $f$ equals some prescribed density $f_0$ or that $f$ belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the…
This paper concerns the problem of applying the generalized goodness-of-fit (gGOF) type tests for analyzing correlated data. The gGOF family broadly covers the maximum-based testing procedures by ordered input $p$-values, such as the false…