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July, 1980 Optimum Kernel Estimators of the Mode
William F. Eddy
Ann. Statist. 8(4): 870-882 (July, 1980). DOI: 10.1214/aos/1176345080

Abstract

Let $X_1, \cdots, X_n$ be independent observations with common density $f$. A kernel estimate of the mode is any value of $t$ which maximizes the kernel estimate of the density $f_n$. Conditions are given restricting the density, the kernel, and the bandwidth under which this estimate of the mode has an asymptotic normal distribution. By imposing sufficient restrictions, the rate at which the mean squared error of the estimator converges to zero can be decreased from $n^{-\frac{4}{7}}$ to $n^{-1+\varepsilon}$ for any positive $\varepsilon$. Also, by bounding the support of the kernel it is shown that for any particular bandwidth sequence the asymptotic mean squared error is minimized by a certain truncated polynomial kernel.

Citation

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William F. Eddy. "Optimum Kernel Estimators of the Mode." Ann. Statist. 8 (4) 870 - 882, July, 1980. https://doi.org/10.1214/aos/1176345080

Information

Published: July, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0438.62027
MathSciNet: MR572631
Digital Object Identifier: 10.1214/aos/1176345080

Subjects:
Primary: 62F10
Secondary: 62G05

Keywords: location of the maximum , parabolic process , polynomial kernel

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 4 • July, 1980
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