Estimating the location of the cauchy distribution by numerical global optimization
作者:
Dallas R. Wingo,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1983)
卷期:
Volume 12,
issue 2
页码: 201-212
ISSN:0361-0918
年代: 1983
DOI:10.1080/03610918308812311
出版商: Marcel Dekker, Inc.
关键词: Cauchy distribution;parameter estimation;miximum likelihood;global optimization;numerical methods
数据来源: Taylor
摘要:
The log-likelihood function (LLF) of the single (location) parameter Cauchy distribution can exhibit up to n relative maxima, where n is the sample size. To compute the maximum likelihood estimate of the location parameter, previously published methods have advocated scanning the LLF over a suf-ficiently large portion of the real line to locate the absolute maximum. This note shows that, given an easily derived upper bound on the second derivative of the negative LLF, Brent's univariate numerical global optimization method can be used to locate the absolute maximum among several relative maxima of the LLF without performing an exhaustive search over the real line.
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