Regression estimation for a rejective sampling procedure - ARCHIVED

Let auxiliary information be available for use in designing of a survey sample. Let the sample selection procedure consist of selecting a probability sample, rejecting the sample if the sample mean of an auxiliary variable is not within a specified distance of the population mean, continuing until a sample is accepted. It is proven that the large sample properties of the regression estimator for the rejective sample are the same as those of the regression estimator for the original selection procedure. Likewise the usual estimator of variance for the regression estimator is appropriate for the rejective sample. In a Monte Carlo experiment, the large sample properties hold for relatively small samples. Also the Monte Carlo results are in agreement with the theoretical orders of approximation. The efficiency effect of the described rejective sampling is o(n-1) relative to regression estimation without rejection, but the effect can be important for particular samples.