Smoothed pseudo-population bootstrap methods with applications to finite population quantiles

TL;DR

This paper develops smoothed pseudo-population bootstrap methods for more accurate variance estimation and confidence intervals of finite population quantiles, extending techniques from i.i.d. contexts to survey sampling frameworks.

Contribution

It introduces a smoothed bootstrap approach for survey sampling, including a bandwidth selection method, improving variance estimation for finite population quantiles.

Findings

Smoothed bootstrap improves variance estimation accuracy.

Bandwidth selection methods enhance practical implementation.

Mixed results on confidence interval coverage.

Abstract

This paper introduces smoothed pseudo-population bootstrap methods for the purposes of variance estimation and the construction of confidence intervals for finite population quantiles. In an i.i.d. context, it has been shown that resampling from a smoothed estimate of the distribution function instead of the usual empirical distribution function can improve the convergence rate of the bootstrap variance estimator of a sample quantile. We extend the smoothed bootstrap to the survey sampling framework by implementing it in pseudo-population bootstrap methods for high entropy, single-stage survey designs, such as simple random sampling without replacement and Poisson sampling. Given a kernel function and a bandwidth, it consists of smoothing the pseudo-population from which bootstrap samples are drawn using the original sampling design. Given that the implementation of the proposed algorithms requires the specification of the bandwidth, we develop a plug-in selection method along with a grid search selection method based on a bootstrap estimate of the mean squared error. Simulation results suggest a gain in efficiency associated with the smoothed approach as compared to the standard pseudo-population bootstrap for estimating the variance of a quantile estimator together with mixed results regarding confidence interval coverage.