Mean Value Estimation Using Two-Phase Samples with Missing Data in Both Phases

The phenomenon of nonresponse in a sample survey reduces the precision of parameter estimates and causes the bias. Several methods have been developed to compensate for these effects. An important technique is the double sampling scheme introduced by Hansen and Hurwitz (J. Am. Stat. Assoc.41, 517–529, 1946) which relies on subsampling of nonrespondents and repeating efforts to collect data from subsampled units. Several generalizations of this procedure have been proposed, including the application of arbitrary sampling designs considered by Särndal et al. (Model Assisted Survey Sampling, 1992). Under the assumption of complete response in the second phase, the population mean estimator constructed using data from both phases is unbiased.