The Annals of Statistics

Asymptotic Number of Roots of Cauchy Location Likelihood Equations

James A. Reeds

Full-text: Open access

Abstract

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

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 775-784.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349554

Digital Object Identifier
doi:10.1214/aos/1176349554

Mathematical Reviews number (MathSciNet)
MR790572

Zentralblatt MATH identifier
0576.62027

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62F12: Asymptotic properties of estimators

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

Citation

Reeds, James A. Asymptotic Number of Roots of Cauchy Location Likelihood Equations. Ann. Statist. 13 (1985), no. 2, 775--784. doi:10.1214/aos/1176349554. https://projecteuclid.org/euclid.aos/1176349554


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