Tilted Nonparametric Regression Function Estimation

TL;DR

This paper introduces a tilted nonparametric regression estimator that improves accuracy and retains desirable properties of kernel estimators, demonstrated through theoretical analysis and empirical studies including COVID-19 data fitting.

Contribution

It develops a new tilted linear smoother estimator with proven convergence rates, enhancing nonparametric regression accuracy over classical methods.

Findings

Tilted estimators outperform classical analogs in MISE under certain conditions.

The proposed estimators effectively fit real-world COVID-19 and dose-response data.

The method maintains the properties of the underlying flat-top kernel estimator.

Abstract

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a nonparametric regression function estimator, which is obtained by minimizing the distance to an infinite order flat-top trapezoidal kernel estimator. We prove that the proposed estimator achieves a high level of accuracy. Moreover, it preserves the attractive properties of the infinite order flat-top kernel estimator. We also present an extensive numerical study for analysing the performance of two members of the tilted linear smoother class named tilted Nadaraya-Watson and tilted local linear in the finite sample. The simulation study shows that tilted Nadaraya-Watson and tilted local linear perform better than their classical analogs in some conditions in terms of Mean Integrated Squared Error (MISE). Finally, the performance of these estimators as well as the conventional estimators were illustrated by curve fitting to COVID-19 data for 12 countries and a dose-response data set.