Related papers: Optimal Function-on-Scalar Regression over Complex…

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…

We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…

Extremiles provide a generalization of quantiles which are not only robust, but also have an intrinsic link with extreme value theory. This paper introduces an extremile regression model tailored for functional covariate spaces. The…

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…

We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…

We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal…

It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or…

This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approximation spaces spanned by local Lagrange functions which are…

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 this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

The approximation of functions in Orlicz space by multivariate operators on simplex is considered. The convergence rate is given by using modulus of smoothness.

We reveal the phenomenon that ``naive'' multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression…

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank of the kernel matrix, and in practice, these…

The functional linear regression model has been widely studied and utilized for dealing with functional predictors. In this paper, we study the Nystr\"om subsampling method, a strategy used to tackle the computational complexities inherent…

Distribution-on-distribution regression considers the problem of formulating and estimating a regression relationship where both covariate and response are probability distributions. The optimal transport distributional regression model…

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…