Feeding back information on ineligibility from sample surveys to the frame - ARCHIVED

It is usually discovered in the data collection phase of a survey that some units in the sample are ineligible even if the frame information has indicated otherwise. For example, in many business surveys a nonnegligible proportion of the sampled units will have ceased trading since the latest update of the frame. This information may be fed back to the frame and used in subsequent surveys, thereby making forthcoming samples more efficient by avoiding sampling ineligible units. On the first of two survey occasions, we assume that all ineligible units in the sample (or set of samples) are detected and excluded from the frame. On the second occasion, a subsample of the eligible part is observed again. The subsample may be augmented with a fresh sample that will contain both eligible and ineligible units. We investigate what effect on survey estimation the process of feeding back information on ineligibility may have, and derive an expression for the bias that can occur as a result of feeding back. The focus is on estimation of the total using the common expansion estimator. An estimator that is nearly unbiased in the presence of feed back is obtained. This estimator relies on consistent estimates of the number of eligible and ineligible units in the population being available.