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We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution.
A stochastic approximation method
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On measures of entropy and information
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Convex Analysis
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Minimization Methods for Non-Differentiable Functions
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Introduction to Optimization
B. T. Polyak · 1987
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On large deviations theory and asymptotically efficient monte carlo estimation
J. S. Sadowsky and J. A. Bucklew · 1990
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Adaptive importance sampling in Monte Carlo integration
M.-S. Oh and J. O. Berger · 1992
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An algorithmic approach to the optimization of importance sampling parameters in digital communication system simulation
M. Devetsikiotis and J. K. Townsend · 1993
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Statistical optimization of dynamic importance sampling parameters for efficient simulation of communication networks
M. Devetsikiotis and J. K. Townsend · 1993
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Stochastic gradient optimization of importance sampling for the efficient simulation of digital communication systems
W. A. Al-Qaq, M. Devetsikiotis, and J. K. Townsend · 1995
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Probability and Measure
P. Billingsley · 1995
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Quick estimation of rare events in stochastic networks
D. Lieber, R. Y. Rubinstein, and D. Elmakis · 1997
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Optimization of computer simulation models with rare events
R. Y. Rubinstein · 1997
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Quick simulation: A review of importance sampling techniques in communication systems
P. J. Smith, M. Shafi, and H. Gao · 1997
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Asymptotically optimal importance sampling and stratification for pricing path-dependent options
P. Glasserman, P. Heidelberger, and P. Shahabuddin · 1999
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Adaptive importance sampling by mixtures of products of beta distributions
A. B. Owen and Y. Zhou · 1999
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The cross-entropy method for combinatorial and continuous optimization
R. Y. Rubinstein · 1999
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Fundamentals of Convex Analysis
J.-B. Hiriart-Urruty and C. Lemaréchal · 2001
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Lectures on Monte Carlo Methods
N. Madras · 2002
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Introductory Lectures on Convex Optimization: A Basic Course
Y. Nesterov · 2004
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Monte Carlo Statistical Methods
C. Robert and G. Casella · 2004
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A tutorial on the cross-entropy method
P.-T. de Boer, D. P. Kroese, S. Mannor, and R. Y. Rubinstein · 2005
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Testing Statistical Hypotheses
E. L. Lehmann and J. P. Romano · 2005
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An adaptive importance sampling technique
T. Pennanen and M. Koivu · 2006
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Convergence of adaptive mixtures of importance sampling schemes
R. Douc, R. Guillin, J.-M. Marin, and C. P. Robert · 2007
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