BAYESIAN ANALYSIS OF TOBIT QUANTILE REGRESSION WITH ADAPTIVE LASSO PENALTY IN HOUSEHOLD EXPENDITURE FOR CIGARETTE CONSUMPTION

Abstract

Tobit Quantile Regression with Adaptive Lasso Penalty is a quantile regression model on censored data that adds Lasso's adaptive penalty to its parameter estimation. The estimation of the regression parameters is solved by Bayesian analysis. Parameters are assumed to follow a certain distribution called the prior distribution. Using the sample information along with the prior distribution, the conditional posterior distribution is searched using the Box-Tiao rule. Computational solutions are solved by the MCMC Gibbs Sampling algorithm. Gibbs Sampling can generate samples based on the conditional posterior distribution of each parameter in order to obtain a posterior joint distribution. Tobit Quantile Regression with Adaptive Lasso Penalty was applied to data on Household Expenditure for Cigarette Consumption in 2011. As a comparison for data analysis, Tobit Quantile Regression was used. The results of data analysis show that the Tobit Quantile Regression model with  Adaptive Lasso Penalty is better than the Tobit Quantile Regression.