Open Access
February 2009 A pseudo empirical likelihood approach for stratified samples with nonresponse
Fang Fang, Quan Hong, Jun Shao
Ann. Statist. 37(1): 371-393 (February 2009). DOI: 10.1214/07-AOS578


Nonresponse is common in surveys. When the response probability of a survey variable Y depends on Y through an observed auxiliary categorical variable Z (i.e., the response probability of Y is conditionally independent of Y given Z), a simple method often used in practice is to use Z categories as imputation cells and construct estimators by imputing nonrespondents or reweighting respondents within each imputation cell. This simple method, however, is inefficient when some Z categories have small sizes and ad hoc methods are often applied to collapse small imputation cells. Assuming a parametric model on the conditional probability of Z given Y and a nonparametric model on the distribution of Y, we develop a pseudo empirical likelihood method to provide more efficient survey estimators. Our method avoids any ad hoc collapsing small Z categories, since reweighting or imputation is done across Z categories. Asymptotic distributions for estimators of population means based on the pseudo empirical likelihood method are derived. For variance estimation, we consider a bootstrap procedure and its consistency is established. Some simulation results are provided to assess the finite sample performance of the proposed estimators.


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Fang Fang. Quan Hong. Jun Shao. "A pseudo empirical likelihood approach for stratified samples with nonresponse." Ann. Statist. 37 (1) 371 - 393, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62003
MathSciNet: MR2488356
Digital Object Identifier: 10.1214/07-AOS578

Primary: 62D05
Secondary: 62G20 , 62G99

Keywords: bootstrap , imputation , Pseudo empirical likelihood , response mechanism

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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