On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

Olivier Cappé, Randal Douc, Eric Moulines and Christian Robert

Scandinavian Journal of Statistics, 2002, vol. 29, issue 4, 615-635

Abstract: While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992), is a simulation‐based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value ϕ of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when ϕ is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, ϕ is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.

Date: 2002
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://doi.org/10.1111/1467-9469.00309

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:29:y:2002:i:4:p:615-635

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().