A pseudo empirical likelihood approach for stratified samples with nonresponse

Details A pseudo empirical likelihood approach for stratified samples with nonresponse A pseudo empirical likelihood approach for stratified samples with nonresponse

2009-03-03

arxiv.org/abs/0903.0481v1

Annals of Statistics 2009, Vol. 37, No. 1, 371-393

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/07-AOS578 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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