Bayesian Estimation of Variance under Fine Stratification via Mean-Variance Smoothing

TL;DR

This paper introduces a Bayesian variance estimator for fine stratification surveys that avoids collapsing strata and uses penalized splines for joint mean-variance smoothing, showing improved performance over existing methods.

Contribution

The paper presents a novel Bayesian variance estimation method employing nonparametric smoothing, eliminating the need for strata collapsing in fine stratification surveys.

Findings

The proposed method performs well in simulations.

It provides more accurate variance estimates.

It yields narrower confidence intervals.

Abstract

Fine stratification survey is useful in many applications as its point estimator is unbiased, but the variance estimator under the design cannot be easily obtained, particularly when the sample size per stratum is as small as one unit. One common practice to overcome this difficulty is to collapse strata in pairs to create pseudo-strata and then estimate the variance. The estimator of variance achieved is not design-unbiased, and the positive bias increases as the population means of the paired pseudo-strata become more variant. The resulting confidence intervals can be unnecessarily large. In this paper, we propose a new Bayesian estimator for variance which does not rely on collapsing strata, unlike the previous methods given in the literature. We employ the penalized spline method for smoothing the mean and variance together in a nonparametric way. Furthermore, we make comparisons with the earlier work of Breidt et al. (2016). Throughout multiple simulation studies and an illustration using data from the National Survey of Family Growth (NSFG), we demonstrate the favorable performance of our methodology.