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We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…

Econometrics · Economics 2020-06-15 Nishanth Dikkala , Greg Lewis , Lester Mackey , Vasilis Syrgkanis

In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary…

Statistics Theory · Mathematics 2018-01-16 François Roueff , Andres Sanchez-Perez

This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…

Statistics Theory · Mathematics 2025-12-30 Gil Kur , Eli Putterman

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…

Statistics Theory · Mathematics 2022-02-25 Peijun Sang , Zuofeng Shang , Pang Du

In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…

Statistics Theory · Mathematics 2013-02-07 Olga Klopp , Marianna Pensky

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

Statistics Theory · Mathematics 2022-03-02 Gaëlle Chagny , Anouar Meynaoui , Angelina Roche

The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…

Statistics Theory · Mathematics 2024-10-25 Haruka Irie , Yasutaka Shimizu

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

Statistics Theory · Mathematics 2020-11-23 Karine Bertin , Nicolas Klutchnikoff

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

Statistics Theory · Mathematics 2011-02-28 Yichao Wu , Jianqing Fan , Hans-Georg Müller

We consider high-dimensional multivariate linear regression models, where the joint distribution of covariates and response variables is a multivariate normal distribution with a bandable covariance matrix. The main goal of this paper is to…

Statistics Theory · Mathematics 2021-03-12 Kwangmin Lee , Kyoungjae Lee , Jaeyong Lee

In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing…

Methodology · Statistics 2026-02-19 Hedayat Fathi , Marzia A. Cremona , Federico Severino

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Numerical Analysis · Mathematics 2018-08-01 Qingping Zhou , Wenqing Liu , Jinglai Li , Youssef M. Marzouk

Even though the statistical theory of linear inverse problems is a well-studied topic, certain relevant cases remain open. Among these is the estimation of functions of bounded variation ($BV$), meaning $L^1$ functions on a $d$-dimensional…

Statistics Theory · Mathematics 2019-05-22 Miguel del Álamo , Axel Munk

In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…

Statistics Theory · Mathematics 2012-07-26 Liugen Xue , Qihua Wang

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these…

Methodology · Statistics 2019-02-12 Xiaoxiao Sun , Pang Du , Xiao Wang , Ping Ma

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

High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…

Methodology · Statistics 2025-11-06 Xingche Guo , Yehua Li , Tailen Hsing

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Statistics Theory · Mathematics 2021-11-01 Keli Guo , Jun Fan , Lixing Zhu

We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…

Information Theory · Computer Science 2015-03-11 Jiantao Jiao , Kartik Venkat , Yanjun Han , Tsachy Weissman

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