Estimation of the r-th derivative of a density function by the tilted kernel estimator

TL;DR

This paper investigates the estimation of the s-th derivative of a density function using the tilted kernel estimator, demonstrating it attains the same convergence rate as wavelet estimators.

Contribution

It shows that the tilted kernel estimator achieves optimal convergence rates for estimating density derivatives, matching wavelet estimator performance.

Findings

Tilted kernel estimator achieves optimal convergence rates.

Estimator performance matches wavelet estimators.

Results are in probability convergence.

Abstract

We consider the problem of estimating the s-th derivative of a density function f by the tilted Kernel estimator introduced in Hall and Doosti (2012). Then we further show this estimator achieves the same convergence rate, in probability, the wavelet estimators achieved as shown in Hall and Patil (1995).