Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice

V. G. Spokoiny

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

We propose a method of adaptive estimation of a regression function which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function f or its derivatives. For instance, in the case of a jump of a regression function, beyond the intervals of length (in order) n-1 log n around change-points the quality of estimation is essentially the same as if locations of jumps were known. The method is fully adaptive and no assumptions are imposed on the design, number and size of jumps. The results are formulated in a nonasymptotic way and can therefore be applied for an arbitrary sample size.

Original languageEnglish
Pages (from-to)1356-1378
Number of pages23
JournalAnnals of Statistics
Volume26
Issue number4
DOIs
Publication statusPublished - Aug 1998
Externally publishedYes

Keywords

  • Change-point
  • Local polynomial fit
  • Local structure
  • Nonparametric regression
  • Pointwise adaptive estimation

Fingerprint

Dive into the research topics of 'Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice'. Together they form a unique fingerprint.

Cite this