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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,…

Machine Learning · Statistics 2025-11-26 Pietro Cappelli , Gaia Grosso , Marco Letizia , Humberto Reyes-González , Marco Zanetti

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…

Statistics Theory · Mathematics 2018-01-23 Jinyuan Chang , Chao Zheng , Wen-Xin Zhou , Wen Zhou

Spatial point processes are used as models in many different fields ranging from ecology and forestry to cosmology and materials science. In recent years, model validation, and in particular goodness-of-fit testing of a proposed point…

Methodology · Statistics 2025-05-20 Chiara Fend , Claudia Redenbach

Given an i.i.d. sample $\{(X_i,Y_i)\}_{i \in \{1 \ldots n\}}$ from the random design regression model $Y = f(X) + \epsilon$ with $(X,Y) \in [0,1] \times [-M,M]$, in this paper we consider the problem of testing the (simple) null hypothesis…

Statistics Theory · Mathematics 2015-02-20 Pierpaolo Brutti

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

Econometrics · Economics 2025-02-04 Jean-Yves Pitarakis

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…

Methodology · Statistics 2020-07-07 Oliver Dukes , Vahe Avagyan , Stijn Vansteelandt

In this work we introduce a new residual for normal linear models that are suitable for situations in which we are dealing with heteroskedasticity of unknown form, they are referred to by principal component analysis (PCA) residuals. These…

Methodology · Statistics 2017-09-01 Andréa V. Rocha , Evelina Shamarova , Alexandre B. Simas

We study the residual bootstrap (RB) method in the context of high-dimensional linear regression. Specifically, we analyze the distributional approximation of linear contrasts $c^{\top} (\hat{\beta}_{\rho}-\beta)$, where…

Statistics Theory · Mathematics 2016-07-05 Miles E. Lopes

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a…

Statistics Theory · Mathematics 2014-02-13 Martin Slawski , Matthias Hein

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression…

Statistics Theory · Mathematics 2009-08-20 Larry Wasserman , Kathryn Roeder

We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…

Methodology · Statistics 2013-01-17 Nicolas Städler , Sach Mukherjee

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

Methodology · Statistics 2009-02-20 Aurore Delaigle , Peter Hall , Tatiyana V. Apanasovich

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Methodology · Statistics 2019-06-25 Jean Feng , Noah Simon

This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…

Statistics Theory · Mathematics 2019-02-12 Gilles R. Ducharme , Pierre Lafaye de Micheaux

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type 1 error…

Methodology · Statistics 2023-10-30 Nikola Surjanovic , Thomas M. Loughin

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a…

Methodology · Statistics 2023-03-09 Maicon J. Karling , Marc G. Genton , Simos G. Meintanis

We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…

Machine Learning · Computer Science 2023-03-15 Francis Bach

Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…

Statistics Theory · Mathematics 2010-07-28 Audrey Finkler

Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…

Statistics Theory · Mathematics 2010-07-28 Audrey Finkler

In population genetics and other application fields, models with intractable likelihood are common. Approximate Bayesian Computation (ABC) or more generally Simulation-Based Inference (SBI) methods work by simulating instrumental data sets…

Methodology · Statistics 2025-01-29 Guillaume Le Mailloux , Paul Bastide , Jean-Michel Marin , Arnaud Estoup