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The estimation problem of minimum mean squared error
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Luc Devroye
Veröffentlicht/Copyright:
25. September 2009
Summary
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.
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Published Online: 2009-09-25
Published in Print: 2003-01-01
© 2003 Oldenbourg Wissenschaftsverlag GmbH
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- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
Artikel in diesem Heft
- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
