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.

中文翻译：

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带有辅助信息的渐近 Z 和卡方检验

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统计检验的效率：Z检验和卡方检验。在统计文献中可以找到许多辅助信息的定义。在本文中，辅助信息的概念是从一个非常笼统的角度讨论的，并且取决于相关的测试。这两个统计测试进行了修改，以便将这些信息考虑在内。特别表明，这些新测试的效率在 Pitman 的 ARE 意义上得到了提高。一些统计示例说明了这种方法的使用。