Nuisance parameter elimination for proportional likelihood ratio models with nonignorable missingness and random truncation

We show that the proportional likelihood ratio model proposed recently by Luo & Tsai (2012) enjoys model-invariant properties under certain forms of nonignorable missing mechanisms and randomly doubletruncated data, so that target parameters in the population can be estimated consistently from t...

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Bibliographic Details
Published in:Biometrika 2013-03, Vol.100 (1), p.269-276
Main Author: CHAN, KWUN CHUEN GARY
Format: Article
Language:English
Subjects:
Estimating techniques
Mathematical models
Maximum likelihood method
Miscellanea
Parameter estimation
Simulation
Studies
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Summary:We show that the proportional likelihood ratio model proposed recently by Luo & Tsai (2012) enjoys model-invariant properties under certain forms of nonignorable missing mechanisms and randomly doubletruncated data, so that target parameters in the population can be estimated consistently from those biased samples. We also construct an alternative estimator for the target parameters by maximizing a pseudolikelihood that eliminates a functional nuisance parameter in the model. The corresponding estimating equation has a U-statistic structure. As an added advantage of the proposed method, a simple score-type test is developed to test a null hypothesis on the regression coefficients. Simulations show that the proposed estimator has a small-sample efficiency similar to that of the nonparametric likelihood estimator and performs well for certain nonignorable missing data problems.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/ass056