BAYESIAN MAXIMUM LIKELIHOOD WITH PARAMETRIC HETEROSCEDASTIC LINEAR MODEL

by Oloyede Isiaka, Ipinyomi R.A and Iyaniwura J.O .

Abstract: We investigate the asymptotic finite properties of maximum likelihood estimator when there is presence of Heteroscedastic in linear regression model. We explore full Bayesian carrying out Markov Chain Monte Carlo simulation. We truncate the model with one component of two sided error structure. A Metropolis-Hasting Algorithm adopted to perform simulation on joint posterior distribution of heteroscedastic linear econometric model. Since Ordinary Least squares is invalid and inefficient when there is presence of heteroscedasticity, the model was conjugated with informative priors to form posterior distribution. Bias and Mean Squares Error criteria were used to evaluate finite properties of the estimator. We chose 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.

Key Words: Markov Chain Monte Carlo Method, Heteroscedasticity, Bayesian Maximum Likelihood Estimator, Asymptotic properties, Metropolis-Hasting Algorithm

Authors:
Oloyede Isiaka, royalinkonsult@gmail.com
Ipinyomi R.A, ipinyomira@yahoo.co.uk
Iyaniwura J.O., jo_iyaniwura@yahoo.com

Editor: Saieed Farag Ateya, said_f_atya@yahoo.com

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