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Biometrika 2001 88(3):727-737; doi:10.1093/biomet/88.3.727
© 2001 by Biometrika Trust
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Case-deletion measures for models with incomplete data

Hongtu Zhu1, Sik-Yum Lee2, Bo-Cheng Wei3 and Julie Zhou4

1 Department of Mathematics and Statistics, University of Victoria, P.O.Box 3045, Victoria, B.C., Canada, V8W 3P4hongtuzhu73{at}hotmail.com 2 Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China. sylee{at}sparc2.sta.cuhk.edu.hk 3 Department of Applied Mathematics, Southeast University, Nanjing 210096, China. bcw{at}seu.edu.cn 4 Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, B.C., Canada, V8W 3P4. jlzhou{at}math.uvic.ca

This paper proposes several case-deletion measures for assessing the influence of an observation for complicated models with real missing data or hypothetical missing data corresponding to latent random variables.The idea is to generalise Cook's (1977) approach to the conditional expectation of the complete-data loglikelihood function in the EM algorithm. On the basis of the diagnostic measures, a procedure is proposed for detecting influential observations. Two examples illustrate our methodology. We show that the method can be applied efficiently to a wide variety of complicated problems that are difficult to handle by existing methods.

Key Words: Case-deletion measure; EM algorithm; Missing data; Q-function

Received June 2000. Revised November 2000


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