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Abstract:
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Skewed data are common in sample surveys. In probability-proportional-to-size sampling, we proposed a Bayesian predictive method for estimating finite population quantiles. We assumed the survey outcome to follow a skew-normal distribution given the observed selection probability. To allow a flexible association between the survey outcome and the probability of selection, we modeled both the location and the scale parameters of the skew-normal distribution as a penalized spline function of the selection probability. Using a fully Bayesian approach, we can obtain the posterior predictive distributions of the non-sample units in the population, and thus the posterior distributions of the finite population quantiles. We showed through simulation that our proposed method is more efficient and yields shorter confidence interval with better confidence coverage than alternative methods in estimating finite population quantiles. We demonstrated the application of our proposed method using a real establishment survey.
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