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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

We propose an adaptive data collection procedure for call prioritization in the context of computer-assisted telephone interview surveys. Our procedure is adaptive in the sense that the effort assigned to a sample unit may vary from one unit to another and may also vary during data collection. The goal of an adaptive procedure is usually to increase quality for a given cost or, alternatively, to reduce cost for a given quality. The quality criterion often considered in the literature is the nonresponse bias of an estimator that is not adjusted for nonresponse. Although the reduction of the nonresponse bias is a desirable goal, we argue that it is not a useful criterion to use at the data collection stage of a survey because the bias that can be removed at this stage through an adaptive collection procedure can also be removed at the estimation stage through appropriate nonresponse weight adjustments. Instead, we develop a procedure of call prioritization that, given the selected sample, attempts to minimize the conditional variance of a nonresponse-adjusted estimator subject to an overall budget constraint. We evaluate the performance of our procedure in a simulation study.

Influential units occur frequently in surveys, especially in the context of business surveys that collect economic variables whose distributions are highly skewed. A unit is said to be influential when its inclusion or exclusion from the sample has an important impact on the magnitude of survey statistics. We extend the results of Beaumont et al. (2013) to the case of two-phase sampling designs. We define the concept of conditional bias attached to a unit with respect to both phases and propose a robust version of the double expansion estimator, which depends on a tuning constant. Following Beaumont et al. (2013), we determine the tuning constant which minimizes the maximum estimated conditional bias. Our results can be naturally extended to the case of unit nonresponse, the set of respondents often being viewed as a second phase sample.

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