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June, 1989 Asymptotic Properties of Kernel Estimators Based on Local Medians
Young K. Truong
Ann. Statist. 17(2): 606-617 (June, 1989). DOI: 10.1214/aos/1176347128

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.

Citation

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Young K. Truong. "Asymptotic Properties of Kernel Estimators Based on Local Medians." Ann. Statist. 17 (2) 606 - 617, June, 1989. https://doi.org/10.1214/aos/1176347128

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0675.62031
MathSciNet: MR994253
Digital Object Identifier: 10.1214/aos/1176347128

Subjects:
Primary: 62G05
Secondary: 62E20

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • June, 1989
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