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Empirical likelihood and Wilks phenomenon for data with nonignorable missing values
Author(s) -
Zhao Puying,
Wang Lei,
Shao Jun
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12379
Subject(s) - empirical likelihood , mathematics , estimator , econometrics , confidence interval , statistics , phenomenon , sample (material) , propensity score matching , point estimation , missing data , physics , chemistry , chromatography , quantum mechanics
Wilks's theorem is useful for constructing confidence regions. When applying the popular empirical likelihood to data with nonignorable nonresponses, Wilks's phenomenon does not hold. This paper unveils that this is caused by the extra estimation of the nuisance parameter in the nonignorable nonresponse propensity. Motivated by this result, we propose an adjusted empirical likelihood for which Wilks's theorem holds. Asymptotic results are presented and supplemented by simulation results for finite sample performance of the point estimators and confidence regions. An analysis of a data set is included for illustration.