High-Frequency Tail Index Estimation by Nearly Tight Frames

TL;DR

This paper investigates the asymptotic behavior of maximum likelihood estimators for spectral parameters of spherical random fields using mexican needlets, and proposes a method to optimize their precision.

Contribution

It introduces a new analysis of estimator properties in high-frequency limits and offers an optimization procedure for estimator accuracy.

Findings

Establishes weak consistency and Gaussianity of estimators

Demonstrates the effectiveness of mexican needlets in spectral estimation

Provides a plug-in method to improve estimator precision

Abstract

This work develops the asymptotic properties (weak consistency and Gaussianity), in the high-frequency limit, of approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. The procedure we used exploits the so-called mexican needlet construction by Geller and Mayeli in [Geller, Mayeli (2009)]. Furthermore, we propose a plug-in procedure to optimize the precision of the estimators in terms of asymptotic variance.