Asymptotic Normality of the Additive Regression Components for Continuous Time Processes

TL;DR

This paper establishes the asymptotic normality and quadratic convergence rate of additive regression components in continuous time processes, addressing the curse of dimensionality in multivariate regression estimation.

Contribution

It extends the additive model framework to continuous time processes, proving asymptotic normality using the marginal integration method.

Findings

Quadratic convergence rate achieved

Asymptotic normality of additive components proven

Addresses curse of dimensionality in continuous time regression

Abstract

In multivariate regression estimation, the rate of convergence depends on the dimension of the regressor. This fact, known as the curse of the dimensionality, motivated several works. The additive model, introduced by Stone (10), offers an efficient response to this problem. In the setting of continuous time processes, using the marginal integration method, we obtain the quadratic convergence rate and the asymptotic normality of the components of the additive model.