Suppose that a statistician observes two independent variates and having densities , . His purpose is to conduct a test for
with a pre-defined significance level . Moran (1973) suggested a test which is based on a single split of the data, i.e., to use in order to conduct a one-sided test in the direction of . Specifically, if and are the ’th and α’th quantiles associated with the distribution of under H, then Moran’s test has a rejection zone
where is a design parameter. Motivated by this issue, the current work includes an analysis of a new notion, regular admissibility of tests. It turns out that the theory regarding this kind of admissibility leads to a simple sufficient condition on and under which Moran’s test is inadmissible.
This work began when the author was a postdoc at the Department of Statistics of The University of Haifa, sponsored by Alexander Goldenshluger. A major part of this work was written when the author was a postdoc at the Department of Statistics and Data-Science of The Hebrew University of Jerusalem, sponsored by Yan Dolinsky with the GIF Grant 1489-304.6/2019.
The author would like to thank Ori Davidov for a discussion which helped in finding the topic for this work. In addition, the author is grateful to Pavel Chigansky for his valuable comments before the submission.
"Simple sufficient condition for inadmissibility of Moran’s single-split test." Electron. J. Statist. 16 (1) 3036 - 3059, 2022. https://doi.org/10.1214/22-EJS2016