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Efficient High-Dimensional Importance Sampling

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  • Jean-Francois Richard

Abstract

The paper describes a simple, generic and yet highly accurate Efficient Importance Sampling (EIS) Monte Carlo (MC) procedure for the evaluation of high-dimensional numerical integrals. EIS is based upon a sequence of auxiliary weighted regressions which actually are linear under appropriate conditions. It can be used to evaluate likelihood functions and byproducts thereof, such as ML estimators, for models which depend upon unobservable variables. A dynamic stochastic volatility model and a logit panel data model with unobserved heterogeneity (random effects) in both dimensions are used to provide illustrations of EIS high numerical accuracy, even under small number of MC draws. MC simulations are used to characterize the finite sample numerical and statistical properties of EIS-based ML estimators.

Suggested Citation

  • Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    • Handle: RePEc:pit:wpaper:321
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    File URL: http://www.econ.pitt.edu/fantin/papers/efficientHD-import-sampling.pdf
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