Non-parametric residual variance estimation in supervised learning

Authors:
Elia Liitiäinen;Amaury Lendasse;Francesco Corona
Affiliations:
Helsinki University of Technology, Lab. of Computer and Information Science, Espoo, Finland;Helsinki University of Technology, Lab. of Computer and Information Science, Espoo, Finland;Helsinki University of Technology, Lab. of Computer and Information Science, Espoo, Finland
Venue:
IWANN'07 Proceedings of the 9th international work conference on Artificial neural networks
Year:
2007

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Abstract

The residual variance estimation problem is well-known in statistics and machine learning with many applications for example in the field of nonlinear modelling. In this paper, we show that the problem can be formulated in a general supervised learning context. Emphasis is on two widely used non-parametric techniques known as the Delta test and the Gamma test. Under some regularity assumptions, a novel proof of convergence of the two estimators is formulated and subsequently verified and compared on two meaningful study cases.