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AdMit: Adaptive Mixtures of Student-t Distributions

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Abstract

This short note presents the R package AdMit which provides flexible functions to approximate a certain target distribution and to efficiently generate a sample of random draws from it, given only a kernel of the target density function. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. To illustrate the use of the package, we apply the AdMit methodology to a bivariate bimodal distribution. We describe the use of the functions provided by the package and document the ability and relevance of the methodology to reproduce the shape of non-elliptical distributions.

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Bibliographic Info

Paper provided by Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland in its series DQE Working Papers with number 10.

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Length: 6 pages
Date of creation: 01 Aug 2008
Date of revision: 07 Jan 2009
Publication status: Published in The R Journal, 2009, vol. 1, no. 1, pp.25--31.
Handle: RePEc:fri:dqewps:wp0010

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Related research

Keywords: adaptive mixture; Student-t distributions; importance sampling; independence chain Metropolis-Hastings algorithm; Bayesian inference; R software.;

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References

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  1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  2. HOOGERHEIDE, Lennart F. & KAASHOEK, Johan F. & van DIJK, Herman K., . "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: an application of flexible sampling methods using neural networks," CORE Discussion Papers RP -1922, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  4. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: the R package AdMit," DQE Working Papers 9, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  5. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Possibly Ill-behaved Posteriors in Econometric Models," Tinbergen Institute Discussion Papers 08-036/4, Tinbergen Institute, revised 18 Apr 2008.
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Cited by:
  1. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling," Tinbergen Institute Discussion Papers 08-092/4, Tinbergen Institute.
  2. David Ardia & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2010. "A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods," Tinbergen Institute Discussion Papers 10-059/4, Tinbergen Institute.
  3. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, . "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, American Statistical Association, vol. 29(i03).
  4. David Ardia & Lennart Hoogerheide & Herman K. van Dijk, 2009. "To Bridge, to Warp or to Wrap? A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods," Tinbergen Institute Discussion Papers 09-017/4, Tinbergen Institute.
  5. Nalan Basturk & Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2012. "The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation," Tinbergen Institute Discussion Papers 12-096/III, Tinbergen Institute.
  6. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, 2008. "Adaptive Mixture of Student-t distributions as a Flexible Candidate Distribution for Efficient Simulation," Tinbergen Institute Discussion Papers 08-062/4, Tinbergen Institute, revised 15 Dec 2008.
  7. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
  8. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  9. BAUWENS, Luc & DUFAYS, Arnaud & DE BACKER, Bruno, 2011. "Estimating and forecasting structural breaks in financial time series," CORE Discussion Papers 2011055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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