Large-sample theory for parametric multiple imputation procedures

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 mcasurement error problem is used to illustrate the results.

[1]  Edward H. Ip,et al.  Stochastic EM: method and application , 1996 .

[2]  Marie Reilly,et al.  Data analysis using hot deck multiple imputation , 1993 .

[3]  R. Fay.  Alternative Paradigms for the Analysis of Imputed Survey Data , 1996 .

[4]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[5]  R D Gill,et al.  Non-response models for the analysis of non-monotone ignorable missing data. , 1997, Statistics in medicine.

[6]  D. McFadden,et al.  ESTIMATION BY SIMULATION , 1994 .

[7]  S Greenland,et al.  A critical look at methods for handling missing covariates in epidemiologic regression analyses. , 1995, American journal of epidemiology.

[8]  Paul A. Ruud,et al.  Extensions of estimation methods using the EM algorithm , 1991 .

[9]  Xiao-Li Meng,et al.  Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm , 1991 .

[10]  G. C. Wei,et al.  A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms , 1990 .

[11]  Nathaniel Schenker,et al.  Asymptotic results for multiple imputation , 1988 .

[12]  Xiao-Li Meng,et al.  Multiple-Imputation Inferences with Uncongenial Sources of Input , 1994 .

[13]  S. Richardson,et al.  Stochastic Algorithms for Markov Models Estimation with Intermittent Missing Data , 1999, Biometrics.

[14]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[15]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[16]  P. J. Huber.  The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[17]  G. Celeux,et al.  Asymptotic properties of a stochastic EM algorithm for estimating mixing proportions , 1993 .

[18]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .