The Annals of Statistics

Asymptotic Properties of Kernel Estimators Based on Local Medians

Young K. Truong

Full-text: Open access

Abstract

The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence $n^{-1/(2+d)}$ both pointwise and in the $L^q (1 \leq q < \infty)$ norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(2+d)}$ in the $L^\infty$ norm restricted to a compact. These results also constitute an answer to an open question of Stone.

Article information

Source
Ann. Statist. Volume 17, Number 2 (1989), 606-617.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347128

Digital Object Identifier
doi:10.1214/aos/1176347128

Mathematical Reviews number (MathSciNet)
MR994253

Zentralblatt MATH identifier
0675.62031

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory

Keywords
Kernel estimator nonparametric regression conditional median function local median rate of convergence

Citation

Truong, Young K. Asymptotic Properties of Kernel Estimators Based on Local Medians. Ann. Statist. 17 (1989), no. 2, 606--617. doi:10.1214/aos/1176347128. http://projecteuclid.org/euclid.aos/1176347128.


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