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In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…

Statistics Theory · Mathematics 2013-05-24 Rida Benhaddou , Marianna Pensky , Dominique Picard

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They…

Statistics Theory · Mathematics 2016-07-25 Shashank Singh , Simon S. Du , Barnabás Póczos

We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…

Machine Learning · Statistics 2019-03-19 Shengyu Zhu , Biao Chen , Pengfei Yang , Zhitang Chen

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…

Statistics Theory · Mathematics 2019-04-18 Feras A. Saad , Cameron E. Freer , Nathanael L. Ackerman , Vikash K. Mansinghka

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…

Statistics Theory · Mathematics 2024-06-11 Antonio Di Noia , Lucio Barabesi , Marzia Marcheselli , Caterina Pisani , Luca Pratelli

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

We consider the problem of testing hypotheses on the copula density from $n$ bi-dimensional observations. We wish to test the null hypothesis characterized by a parametric class against a composite nonparametric alternative. Each density…

Statistics Theory · Mathematics 2009-03-02 Ghislaine Gayraud , Karine Tribouley

We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…

Statistics Theory · Mathematics 2008-02-11 Fabienne Comte , Yves Rozenholc , Marie-Luce Taupin

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the…

Machine Learning · Statistics 2017-10-25 Wittawat Jitkrittum , Wenkai Xu , Zoltan Szabo , Kenji Fukumizu , Arthur Gretton

Goodness-of-Fit tests, including Smooth ones, are introduced and applied to detect non-Gaussianity in Cosmic Microwave Background simulations. We study the power of three different tests: the Shapiro-Francia test (1972), the uncategorised…

Astrophysics · Physics 2009-11-07 L. Cayon , F. Argueso , E. Martinez-Gonzalez , J. L. Sanz

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…

Methodology · Statistics 2023-11-09 Daniela Schkoda , Mathias Drton

It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…

Statistics Theory · Mathematics 2021-01-08 Alexander Goldenshluger , Taeho Kim

If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more precise lower bound, we study semiparametric efficiency in the…

Statistics Theory · Mathematics 2014-05-07 Mathias Trabs

We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, Z=X+\sigma\epsilon$, involving independent and unobserved random variables $X,\xi,\epsilon$. The density $g$ of…

Statistics Theory · Mathematics 2008-02-11 Fabienne Comte , Marie-Luce Taupin

This paper formally derives the asymptotic distribution of a goodness-of-fit test based on the Kernel Stein Discrepancy introduced in (Oscar Key et al., "Composite Goodness-of-fit Tests with Kernels", Journal of Machine Learning Research…

Statistics Theory · Mathematics 2026-02-24 Florian Brück , Veronika Reimoser , Fabian Baier

We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically…

Methodology · Statistics 2017-08-30 Jade Giguelay , Sylvie Huet

The problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a $L_2$-distance comparing a parametric and a nonparametric…

We introduce the \textit{almost goodness-of-fit} test, a procedure to assess whether a (parametric) model provides a good representation of the probability distribution generating the observed sample. Specifically, given a distribution…

Methodology · Statistics 2025-10-15 Amparo Baíllo , Javier Cárcamo

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

Methodology · Statistics 2021-04-28 Sean van der Merwe

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

Statistics Theory · Mathematics 2024-09-04 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy