The estimation problem of minimum mean squared error

Devroye Luc, Schäfer Dominik, Györfi László and Walk Harro

Statistics & Risk Modeling, 2003, vol. 21, issue 1, 15-28

Abstract: 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.

Date: 2003
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DOI: 10.1524/stnd.21.1.15.20315

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