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On the Convergence of Monte Carlo Maximum Likelihood Calculations
 Journal of the Royal Statistical Society B
, 1992
"... Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the ..."
Abstract

Cited by 59 (3 self)
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Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the functions to integrate to one can be approximated by Monte Carlo, the only regularity conditions being a compactification of the parameter space such that the the evaluation maps ` 7! h ` (x) remain continuous. Then with probability one the Monte Carlo approximant to the log likelihood hypoconverges to the exact log likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile, and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painlev'eKuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...
Inconsistency of the MLE for the joint distribution of interval censored survival times
, 2007
"... and continuous marks ..."
unknown title
, 2008
"... Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks ..."
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Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
Maximum Likelihood Estimation
, 2005
"... Maximum likelihood: counterexamples, examples, and open problems ..."
A Loss Function Approach to Model Specification Testing and Its Relative Efficiency to the GLR Test
, 2009
"... The generalized likelihood ratio (GLR) test is proposed by Fan, Zhang and Zhang (2001) as a generally applicable statistical method to test parametric, semiparametric or nonparametric models against nonparametric alternative models. It is a natural extension of the maximum likelihood ratio test for ..."
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The generalized likelihood ratio (GLR) test is proposed by Fan, Zhang and Zhang (2001) as a generally applicable statistical method to test parametric, semiparametric or nonparametric models against nonparametric alternative models. It is a natural extension of the maximum likelihood ratio test for parametric models and fully inherits the advantages of the classical likelihood ratio test. Both true likelihood and pseudo likelihood functions can be used. Like the classical likelihood ratio test, the GLR test enjoys the appealing Wilks phenomena in the sense that its asymptotic distribution is free of nuisance parameters and nuisance functions, and follows a χ2distribution with a known large number of degrees of freedom. It achieves the asymptotically optimal rate of convergence for nonparametric testing problems formulated by Ingster (1993a, 1993b) and Spokoiny (1996). In this paper, we propose a class of new tests based on loss functions, which measure the discrepancies between the fitted values of the null and nonparametric alternative models, and are often more relevant to applications. Like the GLR test, the loss functionbased test is generally applicable and enjoy many appealing features of the GLR test, including the Wilks phenomena. Most importantly,