Sequential adaptive estimators in nonparametric autoregressive models

TL;DR

This paper introduces a sequential adaptive estimation method for nonparametric autoregressive models with Gaussian noise, achieving optimal convergence rates and providing bounds for the minimax risk.

Contribution

It develops a novel sequential kernel estimator for autoregressive functions, optimizing adaptive convergence rates in nonparametric settings.

Findings

Achieves optimal adaptive convergence rate

Provides upper bounds for minimax risk

Demonstrates effectiveness of sequential kernel estimators

Abstract

We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive convergence rate is given as well as the upper bound for the minimax risk.