Empirical Likelihood Approach for Longitudinal Data with Missing Values and Time-Dependent Covariates
Year: 2016
Author: Yan Zhang, Weiping Zhang, Xiao Guo
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 2 : pp. 200–220
Abstract
Missing data and time-dependent covariates often arise simultaneously in longitudinal studies, and directly applying classical approaches may result in a loss of efficiency and biased estimates. To deal with this problem, we propose weighted corrected estimating equations under the missing at random mechanism, followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present. Such procedure improves efficiency over generalized estimation equations approach with working independent assumption, via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption. The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter. The practical performance of our approach is demonstrated through numerical simulations and data analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-AAM-20638
Annals of Applied Mathematics, Vol. 32 (2016), Iss. 2 : pp. 200–220
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: empirical likelihood estimating equations longitudinal data missing at random.