Uniform Function Estimators in Reproducing Kernel Hilbert Spaces

08/16/2021
by   Paul Dommel, et al.
0

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator, which is often derived by employing Gaussian random fields, converges in the mean norm of the reproducing kernel Hilbert space to the conditional expectation and this implies local and uniform convergence of this function estimator. By preselecting the kernel, the problem does not suffer from the curse of dimensionality. The paper analyzes the statistical properties of the estimator. We derive convergence properties and provide a conservative rate of convergence for increasing sample sizes.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/01/2020

On the Improved Rates of Convergence for Matérn-type Kernel Ridge Regression, with Application to Calibration of Computer Models

Kernel ridge regression is an important nonparametric method for estimat...
research
03/29/2023

One-Step Estimation of Differentiable Hilbert-Valued Parameters

We present estimators for smooth Hilbert-valued parameters, where smooth...
research
07/11/2012

Exponential Families for Conditional Random Fields

In this paper we de ne conditional random elds in reproducing kernel Hil...
research
09/15/2011

Sampled forms of functional PCA in reproducing kernel Hilbert spaces

We consider the sampling problem for functional PCA (fPCA), where the si...
research
01/22/2013

The connection between Bayesian estimation of a Gaussian random field and RKHS

Reconstruction of a function from noisy data is often formulated as a re...
research
01/28/2021

Reproducing kernel Hilbert spaces, polynomials and the classical moment problems

We show that polynomials do not belong to the reproducing kernel Hilbert...
research
10/23/2012

Further properties of Gaussian Reproducing Kernel Hilbert Spaces

We generalize the orthonormal basis for the Gaussian RKHS described in M...

Please sign up or login with your details

Forgot password? Click here to reset