Adaptive Optimal Nonparametric Regression and Density Estimation Based on Fourier-Legendre Expansion

TL;DR

This paper introduces adaptive methods for nonparametric regression and density estimation using Fourier-Legendre expansion, achieving asymptotic optimality and adaptability to unknown smoothness levels.

Contribution

It develops new adaptive estimators based on Fourier-Legendre expansion that are asymptotically optimal and can adapt to unknown smoothness in regression and density estimation.

Findings

Estimators are asymptotically optimal.

Methods adapt to unknown smoothness.

Constructs adaptive confidence intervals.

Abstract

Motivated by finance and technical applications, the objective of this paper is to consider adaptive estimation of regression and density distribution based on Fourier-Legendre expansion, and construction of confidence intervals - also adaptive. The estimators are asymptotically optimal and adaptive in the sense that they can adapt to unknown smoothness.