Inference for imputation estimators

We derive an estimator of the asymptotic variance of both single and multiple imputation estimators. We assume a parametric imputation model but allow for non- and semiparametric analysis models. Our variance estimator, in contrast to the estimator proposed by Rubin (1987), is consistent even when the imputation and analysis models are misspecified and incompatible with one another.

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

[2]  I. Meilijson.  A fast improvement to the EM algorithm on its own terms , 1989 .

[3]  J M Taylor,et al.  Estimating the distribution of times from HIV seroconversion to AIDS using multiple imputation. Multicentre AIDS Cohort Study. , 1990, Statistics in medicine.

[4]  Xiao-Li Meng,et al.  The AIDS Epidemic: Estimating Survival After AIDS Diagnosis From Surveillance Data , 1993 .

[5]  Bradley Efron,et al.  Missing Data, Imputation, and the Bootstrap , 1994 .

[6]  J. Robins,et al.  Estimation of Regression Coefficients When Some Regressors are not Always Observed , 1994 .

[7]  Robert E. Fay.  [Multiple-Imputation Inferences with Uncongenial Sources of Input]: Comment , 1994 .

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

[9]  Roderick J. A. Little,et al.  Modeling the Drop-Out Mechanism in Repeated-Measures Studies , 1995 .

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

[11]  R Little,et al.  Intent-to-treat analysis for longitudinal studies with drop-outs. , 1996, Biometrics.

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

[13]  J M Robins,et al.  Non-response models for the analysis of non-monotone non-ignorable missing data. , 1997, Statistics in medicine.

[14]  Myunghee C. Paik,et al.  The generalized estimating equation approach when data are not missing completely at random , 1997 .

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

[16]  J. Robins,et al.  Analysis of semi-parametric regression models with non-ignorable non-response. , 1997, Statistics in medicine.

[17]  J. Robins,et al.  Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. , 1997, Statistics in medicine.

[18]  James M. Robins,et al.  Large-sample theory for parametric multiple imputation procedures , 1998 .

[19]  David J. Spiegelhalter,et al.  Analysis of longitudinal binary data from multiphase sampling , 1998 .

[20]  James M. Robins,et al.  Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models: Rejoinder , 1999 .

[21]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[22]  D. Rubin,et al.  MULTIPLE IMPUTATIONS IN SAMPLE SURVEYS-A PHENOMENOLOGICAL BAYESIAN APPROACH TO NONRESPONSE , 2002 .

[23]  R. Fay.  When Are Inferences from Multiple Imputation Valid ? , 2002 .