Haar Wavelets in Data Analysis

Abstract

One century ago (1910), the Hungarian mathematician Alfred Haar introduced the simplest wavelets in approximation theory, which are now known as the Haar wavelets. This type of wavelets can effectively be used to fit data in statistical applications. It is well known that for a general regression model, it is not easy to write estimations of its parameters in analytical forms. However, regression models generated from the Haar wavelets are easy to compute. In this article, we introduce how to use the Haar wavelets to formulate regression models and to fit data. In addition, we mention some variations of the Haar wavelets and their possible applications.