Estimation of scale functions to model heteroscedasticity by support vector machines

TL;DR

This paper explores how support vector machines can be used to estimate scale functions like MAD and IQR for modeling heteroscedasticity in regression, extending SVM applications beyond location estimation.

Contribution

It introduces a method for estimating scale functions with SVMs, demonstrating the consistency of MAD-type SVMs in heteroscedastic regression models.

Findings

Proves the consistency of MAD-type SVMs for scale estimation

Highlights the importance of scale estimation in heteroscedastic models

Extends SVM applications to conditional variability measurement

Abstract

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions like the conditional median or the conditional mean. We investigate the estimation of scale functions by SVMs when the conditional median is unknown, too. Estimation of scale functions is important e.g. to estimate the volatility in finance. We consider the median absolute deviation (MAD) and the interquantile range (IQR) as measures of scale. Our main result shows the consistency of MAD-type SVMs.