The Annals of Statistics

Uniform Consistency of a Class of Regression Function Estimators

W. Hardle and S. Luckhaus

Full-text: Open access

Abstract

We study a wide class of nonparametric regression function estimators including kernel estimators and robust smoothers. Under different assumptions on the kernel and the sequence of bandwidths, we obtain weak uniform consistency rates on a bounded interval. The uniform consistency is shown in a "stochastic design model" and in a "fixed design model".

Article information

Source
Ann. Statist., Volume 12, Number 2 (1984), 612-623.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346509

Digital Object Identifier
doi:10.1214/aos/1176346509

Mathematical Reviews number (MathSciNet)
MR740915

Zentralblatt MATH identifier
0544.62037

JSTOR
links.jstor.org

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 60E15: Inequalities; stochastic orderings 62F25: Tolerance and confidence regions

Keywords
Regression robust smoothing kernel estimators uniform convergence rates

Citation

Hardle, W.; Luckhaus, S. Uniform Consistency of a Class of Regression Function Estimators. Ann. Statist. 12 (1984), no. 2, 612--623. doi:10.1214/aos/1176346509. https://projecteuclid.org/euclid.aos/1176346509


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