Statistica Sinica 18(2008), 281-297

CONFIDENCE INTERVALS BASED ON SURVEY DATA

WITH NEAREST NEIGHBOR IMPUTATION

Jun Shao and Hansheng Wang

University of Wisconsin$-$Madison and Peking University

Abstract: Nearest neighbor imputation (NNI) is a popular method used to compensate for item nonresponse in sample surveys. Although previous results showed that the NNI sample mean and quantiles are consistent estimators of the population mean and quantiles, large sample inference procedures, such as asymptotic confidence intervals for the population mean and quantiles, are not available. For the population mean, we establish the asymptotic normality of the NNI sample mean and derive a consistent estimator of its limiting variance, which leads to an asymptotically valid confidence interval. For the quantiles, we obtain consistent variance estimators and asymptotically valid confidence intervals using a Bahadur-type representation for NNI sample quantiles. Some limited simulation results are presented to examine the finite-sample performance of the proposed variance estimators and confidence intervals.

Key words and phrases: Bahadur representation, hot deck, mean, quantiles, variance estimation.