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It is shown that a minimum of the variance V(Ŷ HT ) of the Horvitz-Thompson estimator with value zero can be found in the interior of the region of feasible probabilities of selection z i  (0 &lt; z i  &lt; 1; ∑ z i  = 1), if y N /Y &lt; 1/n, where the units i = 1,...,N of the population are ordered according to their values y i  &gt; 0; Y is the total. Other zero-points of the variance can be found by taking units apriori into the sample.

jahrbücher für nationalökonomie und statistik

Minima, Zero-points, Saddle-points and Singularities of the Variance of the Horvitz-Thompson Estimator in Selection With Unequal Probabilities Without Replacement / Minima, Nullpunkte, Sattelpunkte und Singularitäten der Varianz des Horvitz-Thompson Schätzers bei Auswahl mit unterschiedlichen Wahrscheinlichkeiten ohne Zurücklegen