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'e-Kuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...

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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.

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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.

Measurements made by several laboratories may exhibit non-negligible between-laboratory variability, as well as different within-laboratory 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 Mandel-Paule 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...

FCC spectrum auctions sell licenses to provide mobile phone service in designated geographic territories. We empirically measure efficiency in the C block auction, where the continental US was split into 480 licenses, which differs from a common European system of awarding nationwide licenses. Spectrum auctions can be inefficient because of demand reduction and intimidatory collusion. Unfortunately, there is no one standard model of spectrum auctions. In the spirit of Haile and Tamer (2003), we structurally estimate bidder valuations using a necessary condition for equilibrium behavior known as pairwise stability. Pairwise stability holds across a set of spectrum auction models, including models with intimidatory collusion and demand reduction. Using our valuation estimates, we find that the allocation of licenses in the C block was inefficient compared to awarding four large regional licenses to the largest bidders.

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this paper is to estimate the relationship between ad prices and audience size and composition.