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We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…

Methodology · Statistics 2009-12-19 Herve Cardot , Jan Johannes

The work provides an upper estimate of the best accuracy for the problem of reconstructing derivatives based on function values at a given number of points for the functions of Besov classes meeting the mixed Hoelder conditions. In some…

Classical Analysis and ODEs · Mathematics 2014-01-15 S. N. Kudryavtsev

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed…

Statistics Theory · Mathematics 2007-06-13 Iain M. Johnstone , Bernard W. Silverman

We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…

Statistics Theory · Mathematics 2019-11-19 Vladimir Koltchinskii , Mayya Zhilova

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

Methodology · Statistics 2009-05-20 F. Bunea , M. H. Wegkamp , A. E. Ivanescu

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…

Statistics Theory · Mathematics 2013-02-19 Fabienne Comte , Jan Johannes

In the present paper we consider the problem of estimating a three-dimensional function $f$ based on observations from its noisy Laplace convolution. Our study is motivated by the analysis of Dynamic Contrast Enhanced (DCE) imaging data. We…

Methodology · Statistics 2018-07-17 Rida Benhaddou , Marianna Pensky , Rasika Rajapakshage

Consider nonparametric function estimation under $L^p$-loss. The minimax rate for estimation of the regression function over a H\"older ball with smoothness index $\beta$ is $n^{-\beta/(2\beta+1)}$ if $1\leq p<\infty$ and $(n/\log…

Statistics Theory · Mathematics 2015-02-10 Johannes Schmidt-Hieber

Donoho and Johnstone proposed a method from reconstructing an unknown smooth function $u$ from noisy data $u+\zeta$ by translating the empirical wavelet coefficients of $u+\zeta$ towards zero. We consider the situation where the prior…

Statistics Theory · Mathematics 2018-05-29 Gene Ryan Yoo , Houman Owhadi

An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…

We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold $M$, one wants to recover information about the geometry of $M$. Minimax estimators which have been proposed so far all…

Statistics Theory · Mathematics 2021-10-27 Vincent Divol

We investigate the nonparametric bivariate additive regression estimation in the random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically…

Statistics Theory · Mathematics 2022-05-24 Rida Benhaddou , Qing Liu

This paper deals with the study of dependencies between two given events modeled by point processes. In particular, we focus on the context of DNA to detect favored or avoided distances between two given motifs along a genome suggesting…

Statistics Theory · Mathematics 2011-07-22 Laure Sansonnet

In this paper, we study the nonparametric estimation of the density $f_\Delta$ of an increment of a L\'evy process $X$ based on $n$ observations with a sampling rate $\Delta$. The class of L\'evy processes considered is broad, including…

Statistics Theory · Mathematics 2024-11-04 Céline Duval , Taher Jalal , Ester Mariucci

We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…

Statistics Theory · Mathematics 2012-11-16 Victor-Emmanuel Brunel

This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…

Statistics Theory · Mathematics 2016-07-27 Claudio Durastanti

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…

Optimization and Control · Mathematics 2011-07-15 Peter Richtárik , Martin Takáč

We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…

Statistics Theory · Mathematics 2016-01-27 Qiyang Han , Jon A. Wellner

We consider distributed optimization over networks where each agent is associated with a smooth and strongly convex local objective function. We assume that the agents only have access to unbiased estimators of the gradient of their…

Optimization and Control · Mathematics 2021-10-14 Farzad Yousefian , Jayesh Yevale , Harshal D. Kaushik

Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling…

Computation · Statistics 2020-04-08 Matias Quiroz , Minh-Ngoc Tran , Mattias Villani , Robert Kohn , Khue-Dung Dang