×

Bootstrapping sample quantiles based on complex survey data under hot deck imputation. (English) Zbl 1053.62509

Summary: The bootstrap method works for both smooth and nonsmooth statistics, and replaces theoretical derivations by routine computations. With survey data sampled using a stratified multistage sampling design, the consistency of the bootstrap variance estimators and bootstrap confidence intervals was established for smooth statistics such as functions of sample means [J. N. K. Rao and C.-F. J. Wu, J. Am. Stat. Assoc. 83, No. 401, 231–241 (1988; Zbl 0654.62015)]. However, similar results are not available for nonsmooth statistics such as the sample quantiles and the sample low income proportion. We consider a more complicated 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.

MSC:

62D05 Sampling theory, sample surveys
62G09 Nonparametric statistical resampling methods

Citations:

Zbl 0654.62015
PDFBibTeX XMLCite