On Data Sharpening in Nonparametric Autoregressive Models

TL;DR

This paper investigates the effectiveness of data sharpening in reducing bias within nonlinear first order autoregressive models, highlighting its theoretical properties and numerical performance despite serial dependence challenges.

Contribution

It provides a theoretical and numerical analysis of data sharpening's bias reduction capabilities in autoregressive models, a setting less explored compared to independent data.

Findings

Data sharpening reduces bias under mild conditions.

Performance is slightly less favorable with serial dependence.

Compared favorably with existing bias reduction methods.

Abstract

Data sharpening has been shown to reduce bias in nonparametric regression and density estimation. Its performance on nonlinear first order autoregressive models is studied theoretically and numerically in this paper. Although the asymptotic properties of data sharpening are not as favourable in the presence of serial dependence as in bivariate regression with independent responses, it is still found to reduce bias under mild conditions on the autoregression function. Numerical comparisons with the bias reduction method of Cheng et al. (2018) indicate that data sharpening is competitive in this setting.