Bayesian inference for finite population quantiles from unequal probability samples

Area of Science:

• Statistics
• Survey Methodology
• Bayesian Inference

Background:

• Estimating finite population quantiles from survey data with unequal probability sampling presents statistical challenges.
• Existing methods like sample-weighted, ratio, and difference estimators have limitations in accuracy and robustness.

Purpose of the Study:

• To develop and evaluate novel Bayesian methods for robust and efficient inference of finite population quantiles.
• To compare the performance of new methods against established estimators using simulation studies.

Main Methods:

• Two Bayesian methods using penalized spline regression models were developed.
• The first method estimates cumulative distribution functions, while the second predicts non-sampled values using spline-based mean and variance functions.

Main Results:

• Both Bayesian spline methods demonstrated smaller root mean squared errors than traditional estimators.
• The new methods showed increased robustness to model misspecification compared to regression through the origin models.
• For small sample sizes, credible intervals from the new methods achieved closer to nominal confidence coverage.

Conclusions:

• The proposed Bayesian spline-based estimators provide a favorable balance of robustness and efficiency for quantile estimation in unequal probability sampling.
• These methods offer a valuable alternative for survey data analysis, particularly when dealing with smaller sample sizes or potential model misspecification.