BAYESIAN HETERO-LASSO (A GIBBS SAMPLING APPROACH)
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Date
2018-12
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Journal of Science, Technology, Mathematics and Education (JOSTMED), Federal University of Technology, Minna
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.
Description
Collinearity arises from two sources namely model and data based collinearities. Model
based collinearity arises when the model are defined with collinearity structures such as
lasso type estimator of which some tuning and shrinkage parameters are defined not in
ordinary form, these parameters make significant impact on the selection and estimation of
the parameters.
Keywords
LASSO, Bayesian Inference, heteroscedasticity, mulcollinearity and Gibbs sampler
Citation
Oloyede I. (2018), BAYESIAN HETERO-LASSO (A GIBBS SAMPLING APPROACH)Journal of Science, Technology, Mathematics and Education (JOSTMED)