Nonparametric estimators which can be "plugged-in"

Peter J. Bickel*, Ya'acov Ritov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the ratewise minimax rate of convergence on suitable function spaces, while, at the same time, when "plugged-in," estimate efficiently (at a rate of n -1/2 with the best constant) many functionals of the object? For example, can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function? We show that this is impossible for very large sets, for example, expectations of all functions bounded by M < ∞. However, we also show that it is possible for sets as large as indicators of all quadrants, that is, distribution functions. We give appropriate constructions of such estimates.

Original languageEnglish
Pages (from-to)1033-1053
Number of pages21
JournalAnnals of Statistics
Volume31
Issue number4
DOIs
StatePublished - Aug 2003

Keywords

  • Density estimation
  • Efficient estimator
  • Nonparametric regression

Fingerprint

Dive into the research topics of 'Nonparametric estimators which can be "plugged-in"'. Together they form a unique fingerprint.

Cite this