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We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…

Statistics Theory · Mathematics 2018-11-22 Dominique Fourdrinier , Sergey Pergamenshchikov

This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle…

Statistics Theory · Mathematics 2009-09-18 Victor Konev , Serguei Pergamenchtchikov

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…

Statistics Theory · Mathematics 2013-12-13 Mehmet Caner , Anders Bredahl Kock

Adaptive estimation of a quadratic functional over both Besov and $L_p$ balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and $L_p$ balls. An…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models.…

Statistics Theory · Mathematics 2009-09-02 Nicolas Verzelen

We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…

Statistics Theory · Mathematics 2016-01-12 Rajarshi Mukherjee , Eric Tchetgen Tchetgen , James Robins

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

Statistics Theory · Mathematics 2022-09-28 Wenlong Mou , Martin J. Wainwright , Peter L. Bartlett

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…

Statistics Theory · Mathematics 2008-12-18 Leonid Galtchouk , Serguey Pergamenshchikov

In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…

Statistics Theory · Mathematics 2020-05-05 Emmanuel Caron , Jérôme Dedecker , Bertrand Michel

We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…

Statistics Theory · Mathematics 2017-10-09 Olivier Collier , Laëtitia Comminges , Alexandre B. Tsybakov , Nicolas Verzélen

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish…

Statistics Theory · Mathematics 2011-12-13 Li Wang , Xiang Liu , Hua Liang , Raymond J. Carroll

Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…

Statistics Theory · Mathematics 2019-11-18 Frédéric Lavancier , Arnaud Poinas , Rasmus Waagepetersen

Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…

Statistics Theory · Mathematics 2021-07-02 T. Tony Cai , Hongji Wei

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

Statistics Theory · Mathematics 2018-08-30 Keisuke Yano , Fumiyasu Komaki

We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…

Statistics Theory · Mathematics 2026-04-29 Jie Xie , Dongming Huang

We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via…

Statistics Theory · Mathematics 2015-03-04 Agathe Guilloux , Sarah Lemler , Marie-Luce Taupin

We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…

Statistics Theory · Mathematics 2011-06-24 Yannick Baraud , Christophe Giraud , Sylvie Huet

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

Methodology · Statistics 2021-07-07 Dominik Rothenhäusler

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…

Statistics Theory · Mathematics 2010-10-01 Fabienne Comte , Jan Johannes