Multiple imputation refers to a set of stochastic imputation routines aimed at preserving the multivariate features of the data

Multiple imputation refers to a set of stochastic imputation routines aimed at preserving the multivariate features of the data. While single imputation can produce consistent estimates of the parameters of interest, standard errors are difficult to pin down correctly. Rubin (1978) suggested to take several independent realizations of imputation mechanism, and provided the ways to combine the estimates to obtain the point estimates and standard errors valid under "proper imputation" assumptions.

Barnard, J. and X.-L. Meng (1999). Applications of multiple imputation in medical studies: from AIDS to NHANES. Statistical Methods in Medical Research 8 (1), 17-36. http://dx.doi.org/10.1177/096228029900800103

Rubin, D.B. (1978). Multiple Imputations in Sample Surveys -- A Phenomenological Bayesian Approach to Nonresponse. The Proceedings of the Survey Research Methods Section of the American Statistical Association, 20-34.

Rubin, D. B. (1996). Multiple imputation after 18+ years. Journal of the American Statistical Association 91 (434), 473-489. http://dx.doi.org/10.1080/01621459.1996.1047690. This is the special issue of JASA devoted to multiple imputation.

Rubin, D. B. (2004). Multiple Imputation for Nonresponse in Surveys (Wiley Classics Library). Wiley-Interscience.

White, I. R., P. Royston, and A. M. Wood (2011). Multiple imputation using chained equations: Issues and guidance for practice. Statstistics in Medicine. 30 (4), 377-399. http://dx.doi.org/10.1002/sim.4067

Related tags: missing-data.