论文标题
使用辅助信息的渐近测试渐近测试：$ z $检验和卡方测试的情况
Asymptotic relatively more efficient test with auxiliary information: the case of the $Z$-test and the chi-square test
论文作者
论文摘要
本文的主要目的是研究如何使用辅助信息来提高两个著名的统计测试的效率：$ z $ - 检验和卡方检验。辅助信息的许多定义可以在统计文献中找到。在本文中，从非常一般的角度讨论了辅助信息的概念，并取决于相关测试。修改了这两个统计测试，以便考虑到此信息。特别表明，从皮特曼的意义上讲，这些新测试的效率得到了提高。一些统计示例说明了这种方法的使用。
The main goal of this article is to study how an auxiliary information can be used to improve the efficiency of two famous statistical tests: the $ Z$-test and the chi-square test. Many definitions of auxiliary information can be found in the statistical literature. In this article, the notion of auxiliary information is discussed from a very general point of view and depends on the relevant test. These two statistical tests are modified so that this information is taken into account. It is shown in particular that the efficiency of these new tests is improved in the sense of Pitman's ARE. Some statistical examples illustrate the use of this method.
