Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

Abstract

This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the Z-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary to reach a predefined power. The suggested method is computational and some simple statistical applications are presented to illustrate these results. The framework of this work is non-parametric, so it can be applied to any kind of data and any area using statistics.

Optimal use of auxiliary information : information geometry and empirical process

“…For more general classes, the Glivenko-Cantelli and Donsker theorems are established in [2] under stronger assumptions by using the strong approximation results of [7]. In addition, some works have also been done on U-statistics in the presence of auxiliary information [19] and, more recently, on informed statistical tests [4], [5].…”