## The Annals of Statistics

### Asymptotic Properties of Kernel Estimators Based on Local Medians

Young K. Truong

#### 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
https://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

#### 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. https://projecteuclid.org/euclid.aos/1176347128