The Annals of Statistics

On the asymptotic performance of median smoothers in image analysis and nonparametric regression

Inge Koch

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Abstract

For d-dimensional images and regression functions the true object is estimated by median smoothing. The mean square error of the median smoother is calculated using the framework of M-estimation, and an expression for the asymptotic rate of convergence of the mean square error is given. It is shown that the median smoother performs asymptotically as well as the local mean. The optimal window size and the bandwidth of the median smoother are given in terms of the sample size and the dimension of the problem. The rate of convergence is found to decrease as the dimension increases, and its functional dependence on the dimension changes when the dimension reaches 4.

Article information

Source
Ann. Statist., Volume 24, Number 4 (1996), 1648-1666.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298289

Digital Object Identifier
doi:10.1214/aos/1032298289

Mathematical Reviews number (MathSciNet)
MR1416654

Zentralblatt MATH identifier
0867.62031

Subjects
Primary: 62G07: Density estimation 62G20: Asymptotic properties 62G35: Robustness

Keywords
Median smoother asymptotic optimality $M$-estimation

Citation

Koch, Inge. On the asymptotic performance of median smoothers in image analysis and nonparametric regression. Ann. Statist. 24 (1996), no. 4, 1648--1666. doi:10.1214/aos/1032298289. https://projecteuclid.org/euclid.aos/1032298289


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