Related papers: Data-driven goodness-of-fit tests
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…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying…
Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of…
Generative models are increasingly central to scientific workflows, yet their systematic use and interpretation require a proper understanding of their limitations through rigorous validation. Classic approaches struggle with scalability,…
Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately…
Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…
We present a unified approach to goodness-of-fit testing in $\mathbb{R}^d$ and on lower-dimensional manifolds embedded in $\mathbb{R}^d$ based on sums of powers of weighted volumes of $k$-th nearest neighbor spheres. We prove asymptotic…
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…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
Signal-agnostic data exploration based on machine learning could unveil very subtle statistical deviations of collider data from the expected Standard Model of particle physics. The beneficial impact of a large training sample on machine…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster…
Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual…