English
Related papers

Related papers: Robust extrapolation problem for stochastic sequen…

200 papers

The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…

Statistics Theory · Mathematics 2012-02-27 I. Dattner , A. Goldenshluger , A. Juditsky

We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…

Methodology · Statistics 2016-10-05 Anirvan Chakraborty , Victor M. Panaretos

We study the problem of the nonparametric estimation for the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$. From the continuous observation of the sampling path on…

Statistics Theory · Mathematics 2023-10-23 Chiara Amorino , Arnaud Gloter

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

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Statistics Theory · Mathematics 2015-09-25 Markus Reiß , Leonie Selk

Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study…

Methodology · Statistics 2016-01-28 Simeng Qu , Jane-Ling Wang , Xiao Wang

We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…

Statistics Theory · Mathematics 2024-09-24 Shubhada Agrawal , Prashanth L. A. , Siva Theja Maguluri

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which…

Machine Learning · Statistics 2018-05-14 Xi Chen , Yining Wang , Yu-Xiang Wang

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…

Statistics Theory · Mathematics 2008-10-27 Béatrice Laurent , Carenne Ludeña , Clémentine Prieur

The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…

Numerical Analysis · Mathematics 2020-04-24 Vincent Coppé , Daan Huybrechs

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Statistics Theory · Mathematics 2019-10-08 Zhengling Qi , Ying Cui , Yufeng Liu , Jong-Shi Pang

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…

Classical Analysis and ODEs · Mathematics 2009-12-16 Olexandr Nakonechnyi , Yury Podlipenko , Yury Shestopalov

We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…

Optimization and Control · Mathematics 2022-11-16 Hamza Ennaji , Quentin Mérigot , Luca Nenna , Brendan Pass

We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…

Other Condensed Matter · Physics 2017-01-11 Olga Goulko , Andrey S. Mishchenko , Lode Pollet , Nikolay Prokof'ev , Boris Svistunov

In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…

Statistics Theory · Mathematics 2013-09-20 David Källberg , Oleg Seleznjev

This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…

Optimization and Control · Mathematics 2021-10-14 Bin Zhu , Augusto Ferrante , Johan Karlsson , Mattia Zorzi

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

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…

Optimization and Control · Mathematics 2018-03-12 Luis H. R. Alvarez E.

We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…

Probability · Mathematics 2020-01-16 Martin Sauer , Wilhelm Stannat

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Statistics Theory · Mathematics 2023-03-23 Reese Pathak , Martin J. Wainwright , Lin Xiao