Bayesian Monte Carlo Method for Estimating Small Area Complex Parameters Under Unit-Level Models with Skew-Normal Errors

• Activity Number: 503 - Small Area Estimation with Relaxed Modeling Assumptions
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Mamadou Diallo*
• Keywords: Hierarchical Bayes (HB); Monte Carlo, best prediction (EB); complex parameters; unit-level; skew-normal

Abstract

Small Area Estimation (SAE) methods are increasingly used to provide local estimates in support of public policy decisions. Under normality assumption, Molina et al. (2014) developed a hierarchical Bayesian (HB) approach to estimate small area complex parameters, in particular poverty indicators. When the distribution of the variable of interest is asymmetrical, normality-based estimators may be inefficient in terms of MSE, especially for complex parameters. In this paper, we relax the normality assumption and consider a larger family called skew-normal which includes the normal distribution as a special case. The resulting HB method for the skew-normal model only uses Monte Carlo techniques and does not require Markov chain Monte Carlo (MCMC) methods. Avoiding MCMC is important since Monte Carlo methods do not have mixing chains issues. The posterior density has a closed-form expression requiring only the grid method and sampling importance resampling (SIR) technique are used to draw samples from the posterior distribution. Simulation results and application to survey data are presented.