Title: Empirical likelihood method for non-ignorable missing data problems（报告时间：2013.06.21（本周五上午：9:00-10:00）。报告地点：格物楼503（数学系报告厅）)

    Zhong Guan 
     Department of Mathematical Sciences, Indiana University South Bend, South Bend, Indiana 46634, U.S.A.
     
    Jing Qin
     Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases,   Bethesda, Maryland 20892, U.S.A.
     
Abstract:

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies.
It is well known that non-ignorable missing is the most difficult missing data problem where non-ignorable missing data implies that the missing of a response depends on its own value.
In statistical literature, unlike the ignorable missing data problem,
not many papers on non-ignorable missing data are available except for the full parametric model based approach.
In this paper we study a semiparametric non-ignorable missing data problem, where the missing
probability is assumed to be known up to some parameters, but the regression model for the response
variable conditioning on the covariate is not specified. By employing  Owen (1988)'s
empirical likelihood
method we can construct constrained empirical likelihood. It is shown that the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response are
asymptotically normal. Moreover the semiparametric likelihood ratio statistic can be
used to test whether the missing of some of the responses is non-ignorable or completely at random.
The theoretical results are confirmed by a simulation study. As an illustration, the analysis of
a real AIDS trial data set shows that the missing
 of CD4 counts around two years are non-ignorable and the sample mean based on observed data only
is biased.