Multivariate Intensity Estimation via Hyperbolic Wavelet Selection

TL;DR

This paper introduces a novel hyperbolic wavelet-based method for multivariate intensity estimation that mitigates the curse of dimensionality without requiring structural assumptions, supported by theoretical guarantees and an efficient algorithm.

Contribution

It presents a new wavelet selection procedure for high-dimensional intensity estimation with proven adaptivity and practical implementation.

Findings

Oracle inequality established for the estimator

Method adapts to mixed smoothness functions

Algorithm demonstrates reasonable computational complexity

Abstract

We propose a new statistical procedure able in some way to overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models built from hyperbolic biorthogonal wavelet bases. We study its properties in a unifying intensity estimation framework, where an oracle-type inequality and adaptation to mixed smoothness are shown to hold. Besides, we describe an algorithm for implementing the estimator with a quite reasonable complexity.