Variance estimation when donor imputation is used to fill in missing values

Abstract

Donor imputation is frequently used in surveys. However, very few variance estimation methods that take into account donor imputation have been developed in the literature. This is particularly true for surveys with high sampling fractions using nearest donor imputation, often called nearest‐neighbour imputation. In this paper, the authors develop a variance estimator for donor imputation based on the assumption that the imputed estimator of a domain total is approximately unbiased under an imputation model; that is, a model for the variable requiring imputation. Their variance estimator is valid, irrespective of the magnitude of the sampling fractions and the complexity of the donor imputation method, provided that the imputation model mean and variance are accurately estimated. They evaluate its performance in a simulation study and show that nonparametric estimation of the model mean and variance via smoothing splines brings robustness with respect to imputation model misspecifications. They also apply their variance estimator to real survey data when nearest‐neighbour imputation has been used to fill in the missing values. The Canadian Journal of Statistics 37: 400–416; 2009 © 2009 Statistical Society of Canada

An efficient method of estimation for longitudinal surveys with monotone missing data

“…Such contradictory phenomena has been discussed by Rosenbaum (1987), Robins et al (1994), Little and Vartivarian (2005), Kim and Kim (2007), Beaumont and Bocci (2009). See also Henmi and Eguchi (2004).…”

Recent Developments in Dealing with Item Non‐response in Surveys: A Critical Review

“…While we agree that treating the imputed values as if they were observed values tends to lead to variance estimates that are too small (and ultimately to confidence intervals that are too narrow), we believe that this criticism is not justified because it ignores a wide literature on variance estimation procedures for singly imputed data that have been developed in the last two decades in a survey sampling setting, e.g. Rao & Shao (), Särndal (), Shao & Sitter (), Shao & Steel (), Beaumont & Bocci (), Haziza (), Kim & Rao (), among others. Several variance estimation procedures for producing consistent variance estimators are currently available in the literature.…”

“…Zhong & Chen () established the consistency of imputed estimators as well as their asymptotic normality for kernel imputation procedures. Theoretical properties of nearest‐neighbour imputation and predictive mean matching can be found in Chen & Shao (), Beaumont & Bocci (), Yang & Kim (), among others. For nearest‐neighbour imputation, Yang & Kim () showed that , where G is the number of matching variables.…”

“…Deterministic and random linear regression imputation, nearest-neighbour imputation and historical imputation belong to the class of linear imputation procedures (Beaumont & Bissonnette, 2011). Rancourt et al (1994) and Beaumont & Bocci (2009) derived variance estimators under nearest-neighbour imputation. Beaumont et al (2011) studied historical imputation, andBeaumont &Bissonnette (2011) showed that the method of Särndal (1992) can be easily implemented in the context of composite imputation.…”

Non-parametric Variance Estimation Using Donor Imputation Method

“…Donor imputation is a method in which the missing values for one or more variables of a non responding unit (recipient) are replaced by the corresponding values of a responding unit (donor) with no missing value for these variables. It is a variance estimation method which is valid even in the presence of high sampling fractions [1]. However, very few variance estimation methods that take into account donor imputation have been developed.…”