An invariance principle forU-statistics in simple random sampling without replacement

U-statistics, simple random sampling, random non-response,

Minimaxity of Pitman estimators

Generalizing a result of [4], for location parameter families, it was shown by [11], that Pitman estimators are minimax for translation invariant experiments with a Euclidean parameter space. In the present paper this theorem is extended to experiments whose parameter space is homogeneous under the action of a topological group.Pitman estimators invariant experiments minimaxity

Comparing inclusion probabilities and drawing probabilities for rejective sampling and successive sampling

According to a conjecture of Hájek (1981), for successive sampling the variability of the inclusion probabilities is smaller than the variability of the drawing probabilities, and it exceeds the variability of the inclusion probabilities of rejective sampling. A stronger conjecture is motivated and partly proved.Inclusion probabilities drawing probabilities rejective sampling successive sampling