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On the maximum‐likelihood estimator for the location parameter of a cauchy distribution
Author(s) -
Bai Z. D.,
Fu J. C.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315202
Subject(s) - mathematics , cauchy distribution , maximum likelihood , estimator , maximum likelihood sequence estimation , statistics , location parameter , estimation theory , restricted maximum likelihood , distribution (mathematics) , point estimation , likelihood principle , likelihood function , quasi maximum likelihood , mathematical analysis
In the literature of point estimation, the Cauchy distribution with location parameter is often cited as an example for the failure of maximum‐likelihood method and hence the failure of the likelihood principle in general. Contrary to the above notion, we prove that even in this case the likelihood equation has multiple roots and that the maximum‐likelihood estimator (the global maximum) remains as an asymptotically optimal estimator in the Bahadur sense.