Multiwavelet density estimation

TL;DR

This paper introduces multiwavelet bases for density estimation, demonstrating their advantages over traditional wavelets in capturing local features and symmetries in data.

Contribution

It extends wavelet density estimation methods to multiwavelets, improving performance at coarser resolutions and handling local symmetries more effectively.

Findings

Multiwavelet estimators outperform wavelet estimators at coarser resolutions.

Multiwavelets better capture local symmetries in data.

Empirical results show improved density estimation accuracy.

Abstract

Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel density estimators have been the predominant tools of choice, primarily due to their ease of use and mathematical simplicity. More recently, the use of wavelets for density estimation has gained in popularity due to their ability to approximate a large class of functions, including those with localized, abrupt variations. However, a well-known attribute of wavelet bases is that they can not be simultaneously symmetric, orthogonal, and compactly supported. Multiwavelets-a more general, vector-valued, construction of wavelets-overcome this disadvantage, making them natural choices for estimating density functions, many of which exhibit local symmetries around features such as a mode. We extend the methodology of wavelet density estimation to use multiwavelet bases and illustrate several empirical results where multiwavelet estimators outperform their wavelet counterparts at coarser resolution levels.