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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 ..."
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Cited by 72 (5 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...
DIRECTIONS DE MAJORATION D’UNE FONCTION QUASICONVEXE ET APPLICATIONS
"... Abstract. We introduce the convex cone constituted by the directions of majoration of a quasiconvex function. This cone is used to formulate a qualification condition ensuring the epiconvergence of a sequence of general quasiconvex marginal functions in finite dimensional spaces. ..."
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Abstract. We introduce the convex cone constituted by the directions of majoration of a quasiconvex function. This cone is used to formulate a qualification condition ensuring the epiconvergence of a sequence of general quasiconvex marginal functions in finite dimensional spaces.
APPROXIMATION ISSUES ABSTRACT
"... Averaging has a smoothing and convexifying effect. So expectation functionals are ‘usually ’ convex. However, for an important class of expectation functionals that arise in stochastic programs with chance constraints one can obtain no more than quasiconvexity. Approximation questions for this clas ..."
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Averaging has a smoothing and convexifying effect. So expectation functionals are ‘usually ’ convex. However, for an important class of expectation functionals that arise in stochastic programs with chance constraints one can obtain no more than quasiconvexity. Approximation questions for this class of expectation functionals are also being considered. 1 1