Regression with an infinite number of observations applied to estimating the parameters of the stable distribution using the empirical characteristic function

TL;DR

This paper introduces a regression method using an infinite number of observations based on the empirical characteristic function to estimate stable distribution parameters, demonstrating good performance in small samples.

Contribution

It proposes a novel approach that uses all points in an interval for regression, approximating an infinite number of observations for stable distribution parameter estimation.

Findings

Performs well with small sample sizes

Uses all points in an interval for regression

Approximates an infinite number of observations

Abstract

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these points are dependent on the unknown parameters. And using a fixed number of values for t. In this work the results when all points in an interval is used, thus where least squares using an infinite number of observations,is approximated. It was found that this procedure performs good in small samples.