The Annals of Statistics

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

V. G. Spokoiny

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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.

Article information

Ann. Statist., Volume 26, Number 4 (1998), 1356-1378.

First available in Project Euclid: 21 June 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07
Secondary: 62G20: Asymptotic properties

Change-point local polynomial fit local structure nonparametric regression pointwise adaptive estimation


Spokoiny, V. G. Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice. Ann. Statist. 26 (1998), no. 4, 1356--1378. doi:10.1214/aos/1024691246.

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