On estimation of analytic density in L_p

TL;DR

This paper introduces a kernel estimator for analytic density functions and establishes an upper bound on its local minimax risk, confirming a prior conjecture and advancing the theoretical understanding of density estimation in L_p spaces.

Contribution

It proposes a new kernel-type estimator for analytic densities and provides a theoretical upper bound on its minimax risk, supporting existing conjectures.

Findings

Established an upper bound on the local minimax risk for the estimator.

Confirmed a conjecture of Guerre and Tsybakov (1998).

Enhanced theoretical understanding of density estimation in L_p spaces.

Abstract

The problem of estimation of analytic density function using L_p minimax risk is considered. A kernel-type estimator of an unknown density function is proposed and the upper bound on its limiting local minimax risk is established. Our result is consistent with a conjecture of Guerre and Tsybakov (1998) and augments previous work in this area.