Exponential confidence interval based on the recursive Wolverton-Wagner density estimation

TL;DR

This paper develops exponential confidence intervals for the Wolverton-Wagner density estimator, providing non-improvable bounds for the tail distribution of the estimation error in various norms.

Contribution

It introduces new exponential bounds for the tail behavior of the Wolverton-Wagner density estimator within Grand Lebesgue Spaces, enhancing understanding of its deviation properties.

Findings

Derived non-improvable exponential bounds for the tail distribution.

Established error estimates in pointwise and Lebesgue-Riesz norms.

Provided theoretical guarantees for the estimator's deviation behavior.

Abstract

We derive the exponential non improvable Grand Lebesgue Space norm decreasing estimations for tail of distribution for exact normed deviation for the famous recursive Wolverton-Wagner multivariate statistical density estimation. We consider pointwise as well as Lebesgue-Riesz norm error of statistical density of measurement.