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A computationally efficient oracle estimator for additive nonparametric regression with boot-strap confidence intervals

Linton, Oliver, Kim, W and Hengartner, N (1999) A computationally efficient oracle estimator for additive nonparametric regression with boot-strap confidence intervals. Journal of Computational and Graphical Statistics, 8 (2). pp. 278-297. ISSN 1061-8600

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Abstract

This article makes three contributions. First, we introduce a computationally efficient estimator for the component functions in additive nonparametric regression exploiting a different motivation from the marginal integration estimator of Linton and Nielsen. Our method provides a reduction in computation of order n which is highly significant in practice. Second, we define an efficient estimator of the additive components, by inserting the preliminary estimator into a backfitting˙ algorithm but taking one step only, and establish that it is equivalent, in various senses, to the oracle estimator based on knowing the other components. Our two-step estimator is minimax superior to that considered in Opsomer and Ruppert, due to its better bias. Third, we define a bootstrap algorithm for computing pointwise confidence intervals and show that it achieves the correct coverage.

Item Type: Article
Official URL: http://amstat.tandfonline.com/loi/jcgs/
Additional Information: © 1999 American Statistical Association
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation
Sets: Departments > Economics
Collections > Economists Online
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 27 Apr 2007
URL: http://eprints.lse.ac.uk/1270/

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