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Biometrika 2002 89(2):375-388; doi:10.1093/biomet/89.2.375
© 2002 by Biometrika Trust
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Local multiple imputation

Marc Aerts1, Gerda Claeskens2, Niel Hens3 and Geert Molenberghs3

1 Center for Statistics, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium marc.aerts@luc.ac.be 2 Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A.gerda@stat.tamu.edu 3 Center for Statistics, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium niel.hens@luc.ac.begeert.molenberghs@luc.ac.be

Dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships.If such parametric assumptions do not hold, the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results. In this paper, a fully nonparametric and a semiparametric imputation method are studied, both based on local resampling principles. It is shown that the final estimator, based on these local imputations, is consistent under fewer or no parametric assumptions. Asymptotic expressions for bias, variance and mean squared error are derived, showing the theoretical impact of the different smoothing parameters. Simulations illustrate the usefulness and applicability of the method.

Key Words: Bootstrap; Kernel weight; Missing value; Multiple imputation; Nonparametric imputation; Nonresponse; Semiparametric imputation

Received June 2001. Revised August 2001


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