E ciency of bayesian heteroscedastic linear model
No Thumbnail Available
Date
2014
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Journal of Applied Statistical Analysis EJASA, Electron. J. App. Stat. Anal.
Abstract
In order to investigate the asymptotic e ciency of estimators under two
di erent simulation techniques, normal-normal double sided Heteroscedas-
tic error structure was adopted. We explored Direct Monte Carlo method
of Zellner et al. (2010) and Metropolis Hasting Algorithm experiments, an
approach of Markov Chain Monte Carlo.
We truncated the model with one error component of two sided error struc-
ture. A Metropolis-Hasting Algorithm and Direct Monte Carlo adopted to
perform simulation on marginal posterior distribution of heteroscedastic lin-
ear econometric model. Since Ordinary Least squares is invalid and inef-
cient in the presence of heteroscedastic, heteroscedastic linear model was
conjugated with informative priors to form posterior distribution. Maximum
Likelihood Estimation was compared with Bayesian Maximum Likelihood
Estimation, Mean Squares Error criterion was use to identify which esti-
mator and/or simulation method outperform other. We chose the following
sample sizes: 25; 50; 100; and 200. Thus 10,000 simulations with varying
degree of heteroscedastic error structures were adopted. This is subject to
the level of convergence. In the overall, minimum mean squares error criterion revealed improving
performance asymptotically regardless of the degree of heteroscedasticity.
The results showed that Direct Monte Carlo Method outperformed Markov
Chain Monte Carlo Method and Maximum Likelihood Estimator with mini-
mum mean square error at any degree of heteroscedasticity.
Description
Recently, numerous literatures emerged in the eld of Bayesian Statistics; this is due
to the e ort of people like George Casella and Christian Robert, Jim Albert, Reuven
Rubinstein, Dirk Kroese and other numerous researchers who brought into limelight
the simulation techniques of Markov Chain Monte Carlo technique into the eld of
Bayesian Statistics in the early 90s.
Keywords
Markov Chain Monte Carlo Method, Heteroscedasticity, Bayesian Maximum Likelihood Estimator, Metropolis-Hasting Algorithm, Direct Monte Carlo Method.