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

Estimation of scale functions to model heteroscedasticity by support vector machines