Related papers: Optimal-Transport Based Multivariate Goodness-of-F…
In this work, a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response is proposed. The test is based on a generalization to the functional framework of a previous one, designed for the…
A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed…
A method is presented to construct goodness-of-fit statistics in many dimensions for which the distribution of all possible test results in the limit of an infinite number of data becomes Gaussian if also the number of dimensions becomes…
We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…
Assessing model adequacy is a crucial step in regression analysis, ensuring the validity of statistical inferences. For Generalized Functional Linear Models (GFLMs), which are widely used for modeling relationships between scalar responses…
The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…
Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…
Within the nonparametric regression model with unknown regression function $l$ and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis $l=0$ against a…
The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…
Unbinned maximum likelihood is a common procedure for parameter estimation. After parameters have been estimated, it is crucial to know whether the fit model adequately describes the experimental data. Univariate Goodness of Fit procedures…
The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…
This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon a Gaussian process prior distribution are proven to…
We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and…
We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
This paper reviews recent advancements in the application of optimal transport (OT) to multivariate distribution-free nonparametric testing. Inspired by classical rank-based methods, such as Wilcoxon's rank-sum and signed-rank tests, we…
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…
We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the…
We introduce a general framework for testing statistical hypotheses for probability measures supported on finite spaces, which is based on optimal transport (OT). These tests are inspired by the analysis of variance (ANOVA) and its…
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…