Efficient multiply robust imputation in the presence of influential units in surveys

TL;DR

This paper introduces an efficient multiply robust imputation method for surveys that effectively handles influential units, reducing bias and improving estimator stability in the presence of nonresponse.

Contribution

It develops a new multiply robust imputation approach based on conditional bias, enhancing stability and efficiency when influential units are present.

Findings

The proposed method reduces bias in population total estimates.

Simulation results show improved efficiency over traditional methods.

The approach provides robustness against model assumption failures.

Abstract

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.