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64
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 ..."
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Cited by 59 (4 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...
Managing uncertainty in call centers using Poisson mixtures
 Applied Stochastic Models in Business and Industry
, 2001
"... We model a call center as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call center. We compar ..."
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Cited by 30 (4 self)
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We model a call center as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call center. We compare it to the current practice of using a point estimate of the arrival rate (assumed constant) as forecast.
Consistent Estimation Of Mixture Complexity
, 2001
"... ... This article presents a semiparametric methodology yielding almost sure convergence of the estimated number of components to the true but unknown number of components. The scope of application is vast, as mixture models are routinely employed across the entire diverse application range of st ..."
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Cited by 19 (3 self)
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... This article presents a semiparametric methodology yielding almost sure convergence of the estimated number of components to the true but unknown number of components. The scope of application is vast, as mixture models are routinely employed across the entire diverse application range of statistics, including nearly all of the social and experimental sciences.
Penalized Maximum Likelihood Estimator for Normal Mixtures
, 2000
"... The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in pen ..."
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Cited by 12 (3 self)
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The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function. The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted. As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator. Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one.
Advertising Rates, Audience Composition, and Competition in the Network Television Industry
, 1999
"... this paper is to estimate the relationship between ad prices and audience size and composition. ..."
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Cited by 10 (1 self)
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this paper is to estimate the relationship between ad prices and audience size and composition.
Estimation of a Common Mean and Weighted Means Statistics
 Working Paper WP296, National Institute of Standards and Technology, Statistical Engineering Division
, 1996
"... Measurements made by several laboratories may exhibit nonnegligible betweenlaboratory variability, as well as different withinlaboratory variances. Also, the number of measurements made at each laboratory often differ. A question of fundamental importance in the analysis of such data is how to fo ..."
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Cited by 10 (0 self)
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Measurements made by several laboratories may exhibit nonnegligible betweenlaboratory variability, as well as different withinlaboratory variances. Also, the number of measurements made at each laboratory often differ. A question of fundamental importance in the analysis of such data is how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of Standards and Technology (NIST), particularly when certifying standard reference materials. Primary goals of this work are to study the theoretical properties of this method, and to compare it with some alternative methods, in particular to the maximum likelihood estimator. Towards this end, we show that the MandelPaule solution can be interpreted as a simplified version of the maximum likelihood method. A class of weighted means statistics is investigated for situations where the number of laboratories is large. This c...