分层抽样下有效利用辅助信息的信息论方法

An Information-Theoretic Method under Stratified Random Sampling and the Effective Usage of Auxiliary Information

提出了有效使用辅助信息和含在层总体大小中的信息的信息论方法.在分层简单随机抽样下,证明了交叉熵最小化估计量的渐近方差不会比其它估计量的渐近方差大.特别地,当-X已知,-Y的交叉熵最小化估计等价于最优回归估计.还证明了导出的估计比通常的无信息估计有较小的渐近方差,并给出了其方差的刀切法估计及其渐近性质.

In this paper, we propose a cross - entropy minimization approach to making effective use of auxiliary information and incorporating the information on the stratum population sizes naturally. We show that the asymptotic variances of CEME＇ s are smaller than or equal to those of their competitors under stratified simple random saraphng （srs）. In particular, the cross- entropy minimization estimator of Y , when X is known, is asymptotically equivalent to the optimal regression estimator. We prove that the resulting estimates have smaller asymptotic variances than the usual estimate which do not use auxiliary information. The jackknife estimator of the variance and its large sample property are also given