Applying least absolute deviation regression to regression-type estimation of the index of a stable distribution using the characteristic function

TL;DR

This paper introduces a robust least absolute deviation regression method using the empirical characteristic function to estimate the index and scale of stable distributions, outperforming traditional least squares in small samples.

Contribution

It proposes a novel least absolute deviation regression approach with fixed points for stable distribution parameter estimation, demonstrating improved bias and mean square error.

Findings

Least absolute deviation regression reduces bias and MSE.

Iteratively re-weighted least squares enhances robustness.

Method outperforms least squares in small samples.

Abstract

Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic function. The recognized fixed number of points estimation procedure uses ten points in the interval zero to one, and least squares estimation. It is shown that using the more robust least absolute regression based on iteratively re-weighted least squares outperforms the least squares procedure with respect to bias and also mean square error in smaller samples.