期刊
ANNALS OF STATISTICS
卷 37, 期 1, 页码 371-393出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/07-AOS578
关键词
Pseudo empirical likelihood; response mechanism; bootstrap; imputation
资金
- NSF [DMS-04-04535, SES-07-05033]
Nonresponse is common in Surveys. When the response probability of a survey variable Y depends on Y through ail 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 Laid 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 oil 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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