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The estimation problem of minimum mean squared error

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  • Devroye Luc
  • Schäfer Dominik
  • Györfi László
  • Walk Harro

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.

Suggested Citation

  • Devroye Luc & Schäfer Dominik & Györfi László & Walk Harro, 2003. "The estimation problem of minimum mean squared error," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 15-28, January.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:1/2003:p:15-28:n:3
    DOI: 10.1524/stnd.21.1.15.20315
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    References listed on IDEAS

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    1. Harro Walk, 2002. "Almost Sure Convergence Properties of Nadaraya-Watson Regression Estimates," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 201-223, Springer.
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    Cited by:

    1. Liitiäinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.
    2. P. G. Ferrario & H. Walk, 2012. "Nonparametric partitioning estimation of residual and local variance based on first and second nearest neighbours," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1019-1039, December.

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