Empirical likelihood for estimating equations with missing values

Details Empirical likelihood for estimating equations with missing values Empirical likelihood for estimating equations with missing values

2009-03-04

arxiv.org/abs/0903.0726v1

Annals of Statistics 2009, Vol. 37, No. 1, 490-517

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS585 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS585

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable. The empirical likelihood is used to construct a profile likelihood for the parameter of interest. We demonstrate that the proposed nonparametric imputation can remove the selection bias in the missingness and the empirical likelihood leads to more efficient parameter estimation. The proposed method is further evaluated by simulation and an empirical study on a genetic dataset on recombinant inbred mice.

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