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

By Oliver Linton, W Kim and N Hengartner

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

Topics: HB Economic Theory
Publisher: American Statistical Association
Year: 1999
DOI identifier: 10.1080/10618600.1999.10474814
OAI identifier: oai:eprints.lse.ac.uk:1270
Provided by: LSE Research Online
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