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Biometrika Advance Access published online on January 31, 2008
Biometrika, doi:10.1093/biomet/asm094
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© 2008 Biometrika Trust

Articles

Diagnostic measures for empirical likelihood of general estimating equations

Hongtu Zhu and Joseph G. Ibrahim

Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A. hzhu{at}bios.unc.edu ibrahim{at}bios.unc.edu

Niansheng Tang

Department of Statistics, Yunnan University, Kunming, China nstang{at}ynu.edu.cn

Heping Zhang

Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, Connecticut 06520-8034, U.S.A.
Jiangxi Normal University, Nanchang, China heping.zhang{at}yale.edu

Received for publication 1 August 2006. Revision received 1 August 2007.
  Abstract

We develop diagnostic measures for assessing the influence of individual observations when using empirical likelihood with general estimating equations, and we use these measures to construct goodness-of-fit statistics for testing possible misspecification in the estimating equations. Our diagnostics include case-deletion measures, local influence measures and pseudo-residuals. Our goodness-of-fit statistics include the sum of local influence measures and the processes of pseudo-residuals. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our diagnostic measures and goodness-of-fit statistics.

Key Words: Diagnostic measure • Empirical likelihood • Estimating equation • Goodness-of-fit statistic • Resampling method


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