Comparing three bootstrap methods for survey data

TLDR

Bootstrap methods for variance estimation and confidence intervals in complex survey data have been proposed, with the oldest without‑replacement bootstrap (BWO) being limited to simple designs. The study extends the BWO method to accommodate more complex sampling designs. A simulation study compares the extended BWO with the rescaling bootstrap and mirror‑match bootstrap to assess their performance.

Abstract

Abstract Various bootstrap methods for variance estimation and confidence intervals in complex survey data, where sampling is done without replacement, have been proposed in the literature. The oldest, and perhaps the most intuitively appealing, is the without‐replacement bootstrap (BWO) method proposed by Gross (1980). Unfortunately, the BWO method is only applicable to very simple sampling situations. We first introduce extensions of the BWO method to more complex sampling designs. The performance of the BWO and two other bootstrap methods, the rescaling bootstrap (Rao and Wu 1988) and the mirror‐match bootstrap (Sitter 1992), are then compared through a simulation study. Together these three methods encompass the various bootstrap proposals.