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In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…

Statistics Theory · Mathematics 2009-10-07 Angelika Rohde , Lutz Duembgen

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are…

Probability · Mathematics 2013-08-30 Yaozhong Hu , Fei Lu , David Nualart

We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…

Statistics Theory · Mathematics 2022-02-02 Pankaj Bhagwat , Eric Marchand

We develop large sample theory including nonparametric confidence regions for $r$-dimensional ridges of probability density functions on $\mathbb{R}^d$, where $1\leq r<d$. We view ridges as the intersections of level sets of some special…

Statistics Theory · Mathematics 2020-04-24 Wanli Qiao

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…

Statistics Theory · Mathematics 2023-10-17 Matias D. Cattaneo , Yingjie Feng , William G. Underwood

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

Statistics Theory · Mathematics 2025-07-25 Saida Mancer , Abdelhakim Necir , Djamel Meraghni

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…

Statistics Theory · Mathematics 2016-06-24 Matey Neykov , Yang Ning , Jun S. Liu , Han Liu

We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. We use resampling methods to estimate the projection of $s$ onto finite dimensional linear spaces and a model selection procedure to choose an…

Statistics Theory · Mathematics 2010-07-27 Matthieu Lerasle

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some…

Probability · Mathematics 2024-09-10 M. R. Formica , E. Ostrovsky , L. Sirota

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the…

Statistics Theory · Mathematics 2007-06-13 Liang Peng , Yongcheng Qi

Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex…

Statistics Theory · Mathematics 2021-05-20 Sven Klaassen

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

Statistics Theory · Mathematics 2024-05-14 Anne-Marie George

This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…

Econometrics · Economics 2021-07-26 Sebastian Calonico , Matias D. Cattaneo , Max H. Farrell

This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that it is impossible to construct a length-optimal confidence interval satisfying the correct uniform…

Statistics Theory · Mathematics 2022-10-25 Yuya Sasaki , Yulong Wang

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

Statistics Theory · Mathematics 2017-04-03 Hisayuki Tsukuma , Tatsuya Kubokawa

Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition…

Machine Learning · Computer Science 2019-02-21 Marek Petrik , Reazul Hasan Russell

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of…

Probability · Mathematics 2016-09-07 J. C. Breton , C. Houdré , N. Privault

This is the second part of the research project initiated in Cleanthous et al (2024). We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent…

Statistics Theory · Mathematics 2024-05-28 Galatia Cleanthous , Athanasios G. Georgiadis , Oleg V. Lepski

For a general class of priors based on random series basis expansion, we develop the Bayes Lepski's method to estimate unknown regression function. In this approach, the series truncation point is determined based on a stopping rule that…

Statistics Theory · Mathematics 2017-11-21 William Weimin Yoo , Aad W. van der Vaart

We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…

Statistics Theory · Mathematics 2016-12-07 Piero Veronese , Eugenio Melilli