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June, 1990 Fourier Methods for Estimating Mixing Densities and Distributions
Cun-Hui Zhang
Ann. Statist. 18(2): 806-831 (June, 1990). DOI: 10.1214/aos/1176347627

Abstract

Let $X_1, X_2, \cdots$ be iid observations from a mixture density $f(x) = \int f(x \mid \theta)dG(\theta)$, where $f(x \mid \theta)$ is a known parametric family of density functions and $G$ is an unknown distribution function. This paper concerns estimating the mixing density $g = G'$ and the mixing distribution $G$. Fourier methods are used to derive kernel estimators, upper bounds for their rates of convergence and lower bounds for the optimal rate of convergence. Sufficient conditions are given under which the kernel estimators are asymptotically normal. Our estimators achieve the optimal rate of convergence $(\log n)^{-1/2}$ for the normal family and $(\log n)^{-1}$ for the Cauchy family.

Citation

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Cun-Hui Zhang. "Fourier Methods for Estimating Mixing Densities and Distributions." Ann. Statist. 18 (2) 806 - 831, June, 1990. https://doi.org/10.1214/aos/1176347627

Information

Published: June, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0778.62037
MathSciNet: MR1056338
Digital Object Identifier: 10.1214/aos/1176347627

Subjects:
Primary: 62G05
Secondary: 62E20, 62G20

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 2 • June, 1990
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