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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

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The estimation problem of minimum mean squared error

Luc Devroye / Dominik Schäfer / László Györfi / Harro Walk
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.


Regression analysis of a response variable Y requires careful selection of explanatory variables. The quality of a set of explanatory features X=(X(1),...,X(d)) can be measured in terms of the minimum mean squared error


This paper investigates methods for estimating L* from i.i.d. data. No estimate can converge rapidly for all distributions of (X,Y). For Lipschitz continuous regression function E{Y|X=x}, two estimators for L* are discussed: fitting a regression estimate to a subset of the data and assessing its mean residual sum of squares on the remaining samples, and a nearest neighbor cross-validation type estimate.

About the article

Published Online: 2009-09-25

Published in Print: 2003-01-01

Citation Information: Statistics & Decisions/International mathematical Journal for stochastic methods and models, Volume 21, Issue 1/2003, Pages 15–28, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.

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