Bootstrapping Sample Quantiles Based on Complex Survey Data under Hot Deck Imputation

SURVEY DATA UNDER HOT DECK IMPUTATION Jun Shao1 and Yinzhong Chen Department of Statistics, University of Wisconsin-Madison Abstract The bootstrap method works for both smooth and nonsmooth statistics, and replaces theoretical derivations by routine computations. With survey data sampled using a strati ed multistage sampling design, the consistency of the bootstrap variance estimators and bootstrap con dence intervals was established for smooth statistics such as functions of sample means (Rao and Wu, 1988). However, similar results are not available for nonsmooth statistics such as the sample quantiles and the sample low income proportion. We consider a more complicate situation where the data set contains nonrespondents imputed using a random hot deck method. We establish the consistency of the bootstrap procedures for the sample quantiles and the sample low income proportion. Some empirical results are also presented.