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Biometrika 1998 85(4):935-948; doi:10.1093/biomet/85.4.935
© 1998 by Biometrika Trust
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Large-sample theory for parametric multiple imputation procedures

NAISYIN WANG and JAMES M. ROBINS

Department of Statistics, Texas A&M University College Station, Texas 77843, U.S.A.nwang{at}picard.tamu.edu
Department of Epidemiology, Harvard School of Public Health 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A.robins{at}episun1.hamard.edu

We consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the ‘proper’ imputation procedures proposed by Rubin (1978). The asymptotic variance structure of the resulting estimators is provided. This result is used to compare the relative efficiencies of different imputation procedures. It also provides a basis to understand the behaviour of two Monte Carlo iterative estimators, stochastic EM (Celeux & Diebolt, 1985; Wei & Tanner, 1990) and simulated EM (Ruud, 1991). We further develop properties of these estimators when they stop at iteration K with imputation size m. An application to a measurement error problem is used to illustrate the results.

Key Words: Asymptotic distribution • EM algorithm • Loglikelihood score • Measurement error model • Missing data


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