Design-based treatment of unit nonresponse in environmental surveys using calibration weighting

Unit nonresponse is often a problem in sample surveys. It arises when the values of the survey variable cannot be recorded for some sampled units. In this paper, the use of nonresponse calibration weighting to treat nonresponse is considered in a complete design-based framework. Nonresponse is viewed as a fixed characteristic of the units. The approach is suitable in environmental and forest surveys when sampled sites cannot be reached by field crews. Approximate expressions of design-based bias and variance of the calibration estimator are derived and design-based consistency is investigated. Choice of auxiliary variables to perform calibration is discussed. Sen–Yates–Grundy, Horvitz-Thompson, and jackknife estimators of the sampling variance are proposed. Analytical and Monte Carlo results demonstrate the validity of the procedure when the relationship between survey and auxiliary variables is similar in respondent and nonrespondent strata. An application to a forest survey performed in Northeastern Italy is considered.