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Activity Number: 16
Type: Topic Contributed
Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
Sponsor: Section on Survey Research Methods
Abstract - #304255
Title: Inference for Finite Population Quantiles of Non-Normal Survey Data Using Bayesian Mixture of Splines
Author(s): Qixuan Chen*+ and Xuezhou Mao and Michael R. Elliott and Roderick Little
Companies: Columbia University and Columbia University and University of Michigan and University of Michigan/U.S. Census Bureau
Address: 722 West 168th Street, New York, NY, , USA
Keywords: Bayesian inference ; Gibbs sampling ; penalized spline regression ; probability-proportional-to-size sampling

Non-normally distributed data are common in sample surveys. We propose a robust Bayesian model-based estimator for finite population quantiles of non-normal survey data in probability-proportional-to-size sampling. We assume that the probability of inclusion is known for all the units in the finite population. The non-normal distribution of the continuous survey variable is approximated using a mixture of normal distributions, in which both the mean and the variance of the survey variable are modeled as a smooth function of the inclusion probabilities in each mixture component. A full Bayesian approach using the Markov chain Monte Carlo method is developed to obtain the posterior distribution of the finite population quantiles. We compare our proposed estimator with alternative estimators using simulations based on artificial data as well as a real finite population.

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