Improved Asymptotics for Zeros of Kernel Estimates via a Reformulation of the Leadbetter-Cryer Integral

TL;DR

This paper improves the understanding of the expected number of false inflection points in kernel smoothers by reformulating the Leadbetter-Cryer integral, providing more accurate asymptotic estimates in the small noise limit.

Contribution

It introduces a novel reformulation of the Leadbetter-Cryer integral to derive improved asymptotic results for zero crossings of Gaussian processes in kernel estimation.

Findings

More precise asymptotic estimates for zero crossings

Enhanced understanding of false inflection points in kernel smoothers

Reformulation of classical integral for Gaussian process analysis

Abstract

The expected number of false inflection points of kernel smoothers is evaluated. To obtain the small noise limit, we use a reformulation of the Leadbetter-Cryer integral for the expected number of zero crossings of a differentiable Gaussian process.