Computer Modeling of Irregularly Spaced Signals. Statistical Properties of the Wavelet Approximation Using a Compact Weight Function

TL;DR

This paper introduces a modified wavelet analysis algorithm employing a compact weight function, compares its accuracy with bootstrap estimates, and discusses its statistical properties for irregularly spaced signals.

Contribution

It proposes a novel wavelet analysis method using a compact weight function and provides accuracy assessments with statistical and bootstrap methods.

Findings

Compact weight function improves approximation accuracy

Statistical estimates align with bootstrap results

Enhanced wavelet analysis for irregular signals

Abstract

The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the statistically correct expressions for the least squares approximations with an additional weight function are compared with that obtained using the bootstrap method.