A computationally efficient oracle estimator for additive nonparametric regression with bootstrap confidence intervals?

Woocheol Kim, Oliver B. Linton, Niklaus W. Hengartner

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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.

Original languageEnglish
Pages (from-to)278-297
Number of pages20
JournalJournal of Computational and Graphical Statistics
Volume8
Issue number2
DOIs
StatePublished - Jun 1999

Keywords

  • Instrumental variables
  • Kernel estimation
  • Marginal integration

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