Asymptotic Number of Roots of Cauchy Location Likelihood Equations

James A. Reeds

doi:10.1214/aos/1176349554

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Home > Journals > Ann. Statist. > Volume 13 > Issue 2 > Article

June, 1985 Asymptotic Number of Roots of Cauchy Location Likelihood Equations

James A. Reeds

Ann. Statist. 13(2): 775-784 (June, 1985). DOI: 10.1214/aos/1176349554

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Abstract

The number of local maxima of the Cauchy location likelihood function which are not global maxima is asymptotically Poisson distributed with mean parameter $1/\pi.$

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James A. Reeds. "Asymptotic Number of Roots of Cauchy Location Likelihood Equations." Ann. Statist. 13 (2) 775 - 784, June, 1985. https://doi.org/10.1214/aos/1176349554

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Published: June, 1985

First available in Project Euclid: 12 April 2007

zbMATH: 0576.62027

MathSciNet: MR790572

Digital Object Identifier: 10.1214/aos/1176349554

Subjects:

Primary: 62E20

Secondary: 62F12

Keywords: 62-00 , Cauchy likelihood equations , fluctuation inequality , local maxima , Poisson distribution

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Ann. Statist.

Vol.13 • No. 2 • June, 1985

Institute of Mathematical Statistics

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James A. Reeds "Asymptotic Number of Roots of Cauchy Location Likelihood Equations," The Annals of Statistics, Ann. Statist. 13(2), 775-784, (June, 1985)

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