Related papers: Adaptive functional linear regression
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result in substantial bias in the parameter estimators. The nature…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…
We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…
We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…
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…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…
We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…
We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. We define an $m$-th order Spline Highly Adaptive Lasso Minimum Loss…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form $\hat f_\alpha = q_\alpha \left(T^*T\right)T^*Y$, where $Y$ is the available data, $T$ the forward operator,…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
We study the adaptive minimax estimation of non-linear integral functionals of a density and extend the results obtained for linear and quadratic functionals to general functionals. The typical rate optimal non-adaptive minimax estimators…
We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…