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Biometrika Advance Access originally published online on September 16, 2009
Biometrika 2009 96(4):917-932; doi:10.1093/biomet/asp041
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© 2009 Biometrika Trust

Article

A unified approach to linearization variance estimation from survey data after imputation for item nonresponse

Jae Kwang Kim

Department of Statistics, Iowa State University, Ames, Iowa 50011, U.S.A. jkim{at}iastate.edu

J. N. K. Rao

School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada jrao{at}math.carleton.ca

Received for publication 1 March 2008. Revision received 1 February 2009.
  Abstract

Variance estimation after imputation is an important practical problem in survey sampling. When deterministic imputation or stochastic imputation is used, we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach. We provide some applications of the approach to regression imputation, fractional categorical imputation, multiple imputation and composite imputation. Results from a simulation study, under a factorial structure for the sampling, response and imputation mechanisms, show that the proposed linearization variance estimator performs well in terms of relative bias, assuming a missing at random response mechanism.

Key Words: Composite imputation • Fractional imputation • Imputed estimator • Multiple imputation • Regression imputation


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