  Item nonresponse is a common issue in surveys. Because unadjusted estimators
may be biased in the presence of nonresponse, it is common practice to impute
the missing values with the objective of reducing the nonresponse bias as much
as possible. However, commonly used imputation procedures may lead to unstable
estimators of population totals/means when influential units are present in the
set of respondents. In this article, we consider the class of multiply robust
imputation procedures that provide some protection against the failure of
underlying model assumptions. We develop an efficient version of multiply
robust estimators based on the concept of conditional bias, a measure of
influence. We present the results of a simulation study to show the benefits of
the proposed method in terms of bias and efficiency.
