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不等概率抽样中不放回抽样更优的充分条件AI 解读

A challenging theoretical problem in unequal probability sampling is the question which design, sampling with or without replacement, should be implemented. In this context we compare the Horvitz-Thompson estimator with the Hansen-Hurwitz estimator and derive conditions under which the variance of the Horvitz-Thompson estimator is smaller than the variance of the Hansen-Hurwitz estimator. Examples are given showing the validity of these conditions.

不等概率抽样：不放回抽样方差更小的充分条件AI 解读

A challenging theoretical problem in unequal probability sampling is the question which design, sampling with or without replacement, should be implemented. In this context we compare the Horvitz-Thompson estimator with the Hansen-Hurwitz estimator and derive conditions under which the variance of the Horvitz-Thompson estimator is smaller than the variance of the Hansen-Hurwitz estimator. Examples are given showing the validity of these conditions.

固定样本量抽样策略类的完备性AI 解读

A sampling strategy consists of a sampling design and an estimator. Of special importance are strategies combining simple random sampling with the sample mean as an estimator. We consider this class of strategies and the smaller class of strategies with simple random sampling of (almost) fixed sample size. The convexity of the underlying loss function does not imply the completeness of the smaller class. However the strict convexity of the loss function together with the…

Sampford 抽样与不等概率有放回抽样的比较AI 解读

The classical result that simple random sampling without replacement is better than simple random sampling with replacement holds in unequal probability sampling for the sampling procedure of Sampford.