Confidence regions for the multidimensional density in the uniform norm based on the recursive Wolverton-Wagner estimation

TL;DR

This paper develops an optimal confidence region for an unknown density using recursive Wolverton-Wagner estimation, providing exponential tail bounds in both Lebesgue-Riesz and uniform norms.

Contribution

It introduces a new method for constructing confidence regions with exponential tail decay based on recursive Wolverton-Wagner density estimation.

Findings

Confidence regions have exponential tail decay.

Method applies to Lebesgue-Riesz and uniform norms.

Provides theoretical guarantees for the estimation accuracy.

Abstract

We construct an optimal exponential tail decreasing confidence region for an unknown density of distribution in the Lebesgue-Riesz as well as in the uniform} norm, built on the sample of the random vectors based of the famous recursive Wolverton-Wagner density estimation.