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A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions…
We consider a regression model with errors that are a.s. negative. Thus the regression function is not the expected value of the observations but the right endpoint of their support. We develop two goodness-of-fit tests for the hypotheses…
We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a \yao{sufficiently smooth non-linear map}. The observation noise is…
This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…
Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…
The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix…
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…
Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well…
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;…
This article describes an extension of classical \chi^2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its…
In this paper we study goodness-of-fit testing of single-index models. The large sample behavior of certain score-type test statistics is investigated. As a by-product, we obtain asymptotically distribution-free maximin tests for a large…
Let $(Y,(X_i)_{i\in\mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of…
Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterizing the fit of the model to the underlying conditional law of labels given the…
We propose a novel test statistic for testing exogeneity in the functional linear regression model. In contrast to Hausman-type tests in finite dimensional linear regression setups, a direct extension to the functional linear regression…
We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…
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 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…
In clinical trials the comparison of two different populations is a frequently addressed problem. Non-linear (parametric) regression models are commonly used to describe the relationship between covariates as the dose and a response…
Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies…
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…