Alpha Estimation via Sample Splitting: A Two-Sample Framework for Stable-like Distributions

Fuente: arXiv
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Main Authors: Potgieter, Cornelis J., van Appel, Jacques, Samaratunga, Sudharshan
Format: Preprint
Published: 2017
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author Potgieter, Cornelis J.
van Appel, Jacques
Samaratunga, Sudharshan
author_facet Potgieter, Cornelis J.
van Appel, Jacques
Samaratunga, Sudharshan
contents Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $α$ quantifying tail heaviness. We propose a new semiparametric estimator for $α$ that leverages the two-sum closure property of stable distributions within a location-scale framework. The method transforms a single sample into two pseudo-independent samples via repeated random splitting and estimates $α$ using weighted least squares applied to empirical quantiles. This approach avoids intractable likelihood calculations, offers computational advantages over maximum likelihood estimation, and remains robust to skewness. We establish consistency and asymptotic properties of the estimator and assess its finite-sample performance via simulation. Results indicate competitive accuracy, particularly in small samples and heavy-tailed settings, with substantial computational savings.
format Preprint
id arxiv_https___arxiv_org_abs_1705_09840
institution arXiv
publishDate 2017
record_format arxiv
spellingShingle Alpha Estimation via Sample Splitting: A Two-Sample Framework for Stable-like Distributions
Potgieter, Cornelis J.
van Appel, Jacques
Samaratunga, Sudharshan
Methodology
Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $α$ quantifying tail heaviness. We propose a new semiparametric estimator for $α$ that leverages the two-sum closure property of stable distributions within a location-scale framework. The method transforms a single sample into two pseudo-independent samples via repeated random splitting and estimates $α$ using weighted least squares applied to empirical quantiles. This approach avoids intractable likelihood calculations, offers computational advantages over maximum likelihood estimation, and remains robust to skewness. We establish consistency and asymptotic properties of the estimator and assess its finite-sample performance via simulation. Results indicate competitive accuracy, particularly in small samples and heavy-tailed settings, with substantial computational savings.
title Alpha Estimation via Sample Splitting: A Two-Sample Framework for Stable-like Distributions
topic Methodology
url https://arxiv.org/abs/1705.09840