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In this paper the variance of the Horvitz-Thompson estimator is minimized by an iterative method with the help of spline functions. As result an objective rule is given, how many of the units with greatest size must be taken apriori into the sample.

jahrbücher für nationalökonomie und statistik

A Method of Minimizing the Variance of the Horvitz-Thompson Estimator in Selection with Unequal Probabilities without Replacement / Ein Verfahren zur Minimierung der Varianz des Horvitz-Thompson Schätzers bei Auswahl mit unterschiedlichen Wahrscheinlichkeiten ohne Zurücklegen