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比率策略的渐近极小极大性AI 解读

The use of simple random sampling together with ratio estimation is of fundamental importance in survey sampling practice. From a theoretical point of view the ratio estimator has been justified by Bayesian methods (Ericson, 1969) and by superpopulation methods (Royall, 1970). But these methods do not yield a rigorous justification of simple random sampling at the same time. We use the minimax principle in an asymptotic version to justify both simple random sampling and…

比率策略的渐近极小极大性AI 解读

The use of simple random sampling together with ratio estimation is of fundamental importance in survey sampling practice. From a theoretical point of view the ratio estimator has been justified by Bayesian methods (Ericson, 1969) and by superpopulation methods (Royall, 1970). But these methods do not yield a rigorous justification of simple random sampling at the same time. We use the minimax principle in an asymptotic version to justify both simple random sampling and…

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…

调查抽样中随机化与估计的极小极大方法AI 解读

We consider a finite set of units, a population. With each unit is associated a real value (unknown to us) and a label (identifying the unit). Based on the labels we may select a sample, i.e., a subset of the population, to estimate the mean of the real values. In simple random sampling (not necessarily of fixed size) the selection probabilities of all samples are not affected by a permutation of the labels. It is assumed that we have to choose both a sampling design and a…