Mathematics – Statistics Theory
Scientific paper
2010-11-11
Annals of Statistics 2010, Vol. 38, No. 5, 2823-2856
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/10-AOS807 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/10-AOS807
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305--320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper.
No associations
LandOfFree
Trajectory averaging for stochastic approximation MCMC algorithms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trajectory averaging for stochastic approximation MCMC algorithms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trajectory averaging for stochastic approximation MCMC algorithms will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-430672