Risk upper bounds for RKHS ridge group sparse estimator in the regression model with non-Gaussian and non-bounded error

TL;DR

This paper derives risk upper bounds for a RKHS ridge group sparse estimator in a regression setting with non-Gaussian, unbounded errors, advancing understanding of estimator performance under complex error conditions.

Contribution

It introduces new risk bounds for a RKHS-based estimator in non-Gaussian, unbounded error models, extending previous theoretical results.

Findings

Established upper bounds for empirical $L^2$ risk.

Derived bounds for the $L^2$ risk of the estimator.

Analyzed estimator performance in complex error environments.

Abstract

We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to an additive decomposition including the variables and interactions between them. The estimator of this meta-model is calculated by minimizing an empirical least-squares criterion penalized by the sum of the Hilbert norm and the empirical $L^2$-norm. In this context, the upper bounds of the empirical $L^2$ risk and the $L^2$ risk of the estimator are established.