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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.

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File URL: http://www.econ.pitt.edu/fantin/papers/efficientHD-import-sampling.pdf
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Bibliographic Info

Paper provided by University of Pittsburgh, Department of Economics in its series Working Papers with number 321.

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Date of creation: Jun 2007
Date of revision: Jan 2007
Publication status: Forthcoming in Journal of Econometrics
Handle: RePEc:pit:wpaper:321

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  1. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
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  3. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
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  7. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis.
  8. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  9. BAUWENS, Luc & HAUTSCH, Nikolaus, . "Stochastic conditional intensity processes," CORE Discussion Papers RP -1937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Gourieroux, Christian & Monfort, Alain, 1993. "Simulation-based inference : A survey with special reference to panel data models," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 5-33, September.
  11. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Estimation of Dynamic Bivariate Mixture Models: Comments on Watanabe (2000)," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 570-76, October.
  12. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  13. Lee Kai Ming & Koopman Siem Jan, 2004. "Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-17, May.
  14. Francis Vella & Marno Verbeek, 1998. "Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 163-183.
  15. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  16. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier.
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