BAYESIAN HETERO-LASSO (A GIBBS SAMPLING APPROACH)

Abstract

The study investigates the asymptotic consistency and efficiency of Bayesian estimator due to violation of homoscedasticity cum non-multicollinearity properties. Mean Square Error( MSE) and Bias were the performance measuring criteria on twin non-spherical disturbances. The seed was to 12345; were set at = 2.5,1.5,1,0,0,0.5 ; Xs variables as design matrix was generated from the multivariate normal distribution with > 0 and

. and were contaminated with Harvey (1976) heteroscedastic error structure; ,… were collinear covariate with pairwise correlation of 0.9, the sample sizes were set as 25, 50,70,100,200,500 and 1000. The number of replications of the experiment was set at 11,000 with burn-in of 1000 which specified the draws that were discarded to remove the effect of the initial values. The thinning was set at 5 to ensure the removal of the effect of autocorrelation in our MCMC simulation. In this paper, the study was able to depict the asymptotic consistency and efficiency of the hetero-lasso estimator at large sample sizes, the study affirmed that Bayesian hetero-lasso estimator performed well when the sample size is large. The outcome of the study revealed improved performances of the estimator in the model parameter estimates asymptotically.