English
Related papers

Related papers: Efficient estimation of functionals in nonparametr…

200 papers

We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…

Statistics Theory · Mathematics 2023-04-25 Maksym Luz , Mikhail Moklyachuk

We consider the non-parametric regression problem under Huber's $\epsilon$-contamination model, in which an $\epsilon$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median…

Statistics Theory · Mathematics 2018-05-29 Simon S. Du , Yining Wang , Sivaraman Balakrishnan , Pradeep Ravikumar , Aarti Singh

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process is considered. Estimates are based on observations of the…

Statistics Theory · Mathematics 2025-11-11 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Statistics Theory · Mathematics 2016-11-18 XuanLong Nguyen , Martin J. Wainwright , Michael I. Jordan

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

Statistics Theory · Mathematics 2011-12-19 J. Johannes , R. Schenk

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

Statistics Theory · Mathematics 2021-02-11 Leonie Selk , Charles Tillier , Orlando Marigliano

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

Statistics Theory · Mathematics 2007-06-13 Eric Moulines , Pierre Priouret , François Roueff

In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…

Statistics Theory · Mathematics 2025-05-29 Oliver Y. Feng , Yu-Chun Kao , Min Xu , Richard J. Samworth

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

Statistics Theory · Mathematics 2009-09-29 Jérémie Bigot , Rolando Biscay , Jean-Michel Loubes , Lilian Muniz Alvarez

In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…

Statistics Theory · Mathematics 2015-08-18 Tony Cai , Adityanand Guntuboyina , Yuting Wei

We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…

Statistics Theory · Mathematics 2019-07-16 Martin Kroll

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand…

Data Analysis, Statistics and Probability · Physics 2009-09-28 Jason H. Steffen , Michael W. Moore , Paul E. Boynton

Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…

Statistics Theory · Mathematics 2013-01-16 Elodie Brunel , André Mas , Angelina Roche

The paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic H\"older class estimator. Next applying…

Statistics Theory · Mathematics 2012-07-24 M. Chichignoud

Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…

Econometrics · Economics 2025-10-21 Jing Kong

Existing identification and estimation methods for semiparametric sample selection models rely heavily on exclusion restrictions. However, it is difficult in practice to find a credible excluded variable that has a correlation with…

Econometrics · Economics 2024-12-03 Zhewen Pan , Yifan Zhang

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Methodology · Statistics 2026-02-10 Omiros Papaspiliopoulos , Timothée Stumpf-Fétizon , Jonathan Weare

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Methodology · Statistics 2011-03-31 Guillaume Bouchard , Stéphane Girard , Anatoli Iouditski , Alexander Nazin

The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…

Statistics Theory · Mathematics 2009-08-24 Anatoli B. Juditsky , Arkadi S. Nemirovski

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix…

Statistics Theory · Mathematics 2021-02-12 Jianqing Fan , Haolei Weng , Yifeng Zhou