论文标题
抽样设计的指数不平等
Exponential inequalities for sampling designs
论文作者
论文摘要
在这项工作中，我们介绍了一种一般方法，基于采样设计和Azuma-Hoeffding的不平等的婚姻表示，以导致指数不平等，以使Horvitz-Thompson估计器与其期望之间的差异。应用这个想法，我们为Chao的程序建立了这种不平等，直到{é}的消除程序，广义的Midzuno方法以及Brewer的方法。作为副产品，我们证明了前三个采样设计（有条件地）是负相关的。对于此类采样设计，我们表明，我们获得的不平等通常比应用已知结果对负相关的随机变量而获得的不平等明显。
In this work we introduce a general approach, based on the mar-tingale representation of a sampling design and Azuma-Hoeffding's inequality , to derive exponential inequalities for the difference between a Horvitz-Thompson estimator and its expectation. Applying this idea, we establish such inequalities for Chao's procedure, Till{é}'s elimination procedure, the generalized Midzuno method as well as for Brewer's method. As a by-product, we prove that the first three sampling designs are (conditionally) negatively associated. For such sampling designs, we show that that the inequality we obtain is usually sharper than the one obtained by applying known results for negatively associated random variables.
