## The Annals of Statistics

### Change point estimation using nonparametric regression

#### Abstract

We consider a regression model in which the mean function may have a discontinuity at an unknown point. We propose an estimate of the location of the discontinuity based on one-side nonparametric regression estimates of the mean function. The change point estimate is shown to converge in probability at rate $O(n^{-1})$ and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models. Confidence regions for the location and size of the change are also discussed.

#### Article information

Source
Ann. Statist. Volume 24, Number 4 (1996), 1667-1678.

Dates
First available in Project Euclid: 17 September 2002

http://projecteuclid.org/euclid.aos/1032298290

Digital Object Identifier
doi:10.1214/aos/1032298290

Mathematical Reviews number (MathSciNet)
MR1416655

Zentralblatt MATH identifier
0867.62033

Subjects
Primary: 62G07: Density estimation

#### Citation

Loader, Clive R. Change point estimation using nonparametric regression. Ann. Statist. 24 (1996), no. 4, 1667--1678. doi:10.1214/aos/1032298290. http://projecteuclid.org/euclid.aos/1032298290.

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• MURRAY HILL, NEW JERSEY 07974-2070 E-MAIL: clive@bell-labs.com