Sequential robust efficient estimation for nonparametric autoregressive models

TL;DR

This paper develops efficient, robust sequential estimators for nonparametric autoregressive models, achieving optimal convergence rates similar to regression models, and proposes an adaptive procedure for Gaussian cases.

Contribution

It introduces a new class of sequential estimators for nonparametric autoregression and establishes their optimal convergence rates, including an adaptive method for Gaussian models.

Findings

Achieved minimax convergence rates for nonparametric autoregression.

Proposed an adaptive procedure for Gaussian models.

Demonstrated rates match those of regression models.

Abstract

We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the constructed sequential estimators. The minimax nonadaptive and adaptive convergence rates are established. It turns out that in this case these rates are the same as for regression models.