Related papers: On the Optimality of Functional Sliced Inverse Reg…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an…

We propose a method to remedy finite sample coverage problems and improve upon the efficiency of commonly employed procedures for the construction of nonparametric confidence intervals in regression kink designs. The proposed interval is…

We propose a nested reduced-rank regression (NRRR) approach in fitting regression model with multivariate functional responses and predictors, to achieve tailored dimension reduction and facilitate interpretation/visualization of the…

A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse…

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…

Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…

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…

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

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…

We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…

This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…

We study prediction in the functional linear model with functional outputs : $Y=SX+\epsilon $ where the covariates $X$ and $Y$ belong to some functional space and $S$ is a linear operator. We provide the asymptotic mean square prediction…

We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…

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…

Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…

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…