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Adaptive mixture of Student-t distributions as a flexible distribution for efficient simulation: The R package AdMit

David Ardia, Lennart Hoogerheide & Herman Van Dijk

Résumé This paper 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 core algorithm consists of the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest. Then, importance sampling or the independence chain Metropolis-Hastings algorithm is used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach.
   
Mots-clés Adaptive mixture, Student-t distributions, importance sampling, independence chain Metropolis-Hasting algorithm, Bayesian, R software
   
Citation Ardia, D., Hoogerheide, L., & Van Dijk , H. (2009). Adaptive mixture of Student-t distributions as a flexible distribution for efficient simulation: The R package AdMit. Journal of Statistical Software, 29(3), 1-32.
   
Type Article de périodique (Anglais)
Date de publication 2009
Nom du périodique Journal of Statistical Software
Volume 29
Numéro 3
Pages 1-32
URL https://www.jstatsoft.org/article/view/v029i03
Liée au projet Bayesian estimation of regime-switching GARCH models