Likelihood Principle and Maximum Likelihood Estimator of Location Parameter for Cauchy Distribution

摘要

In the literature of point estimation, Cauchy distribution with location parameters was often cited as an example for the failure of maximum likelihood method and hence the failure of likelihood principle in general. Contrary to the above notion, we proved, even in this case that the likelihood equation has multiple roots, that the maximum likelihood estimator (the global maximum) remains as an asymptotically optimal estimator in the Bahadur sense. (Author)