Bayesian Generalized Least Squares with Parametric Heteroscedasticity Linear Model

• Published in: Asian journal of mathematics & statistics 2013-06, Vol.6 (2), p.67-67
• Main Authors: Isiaka, Oloyede, Ipinyomi, R A, Iyaniwura, J O
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Computer simulation; Errors; Estimators; Mathematical models; Samples; Statistical analysis; Statistical methods
• ISSN: 1994-5418; 2077-2068
• DOI: 10.3923/ajms.2013.67.75

We investigate the asymptotic finite properties of estimator to ascertain its behaviour from small to large sample when there is presence of heteroscedasticity. We explore full Bayesian experiments with Generalized Least Squares estimator incorporating heteroscedastic error structure. Estimates were obtained through Markov Chain Monte Carlo approach that draws simulated sample of parameters from joint posterior distribution. Burnin and thinning were chosen as 1000 and 5, respectively. Bias and Mean Squares Error criteria were used to evaluate finite properties of the estimator. We choose the following sample sizes: 25, 50, 100, 200, 500 and 1000. Thus, 10,000 simulations with varying degree of heteroscedasticity were carried out. This is subjected to the level of convergence. Bias and Minimum Mean Squares Error criteria revealed improving performance asymptotically regardless of the degree of heteroscedasticity. Considering heteroscedasticity at scale 0.3, from the results, we observed an increase in sample sizes: 25, 50, 100, 200, 500 and 1000 led to decrease in mean squares error: 0.068436, 0.033896, 0.015071, 0.006772, 0.001935 and 0.00101, respectively. This implies efficiency of the estimator asymptotically, ditto for all other scales.