Open Access
2022 Simple sufficient condition for inadmissibility of Moran’s single-split test
Royi Jacobovic
Author Affiliations +
Electron. J. Statist. 16(1): 3036-3059 (2022). DOI: 10.1214/22-EJS2016


Suppose that a statistician observes two independent variates X1 and X2 having densities fi(;θ)fi(θ),i=1,2, θR. His purpose is to conduct a test for


with a pre-defined significance level α(0,1). Moran (1973) suggested a test which is based on a single split of the data, i.e., to use X2 in order to conduct a one-sided test in the direction of X1. Specifically, if b1 and b2 are the (1α)’th and α’th quantiles associated with the distribution of X2 under H, then Moran’s test has a rejection zone


where aR 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 f1() and f2() under which Moran’s test is inadmissible.

Funding Statement

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.


Download Citation

Royi Jacobovic. "Simple sufficient condition for inadmissibility of Moran’s single-split test." Electron. J. Statist. 16 (1) 3036 - 3059, 2022.


Received: 1 March 2021; Published: 2022
First available in Project Euclid: 4 May 2022

MathSciNet: MR4416679
zbMATH: 1493.62033
Digital Object Identifier: 10.1214/22-EJS2016

Primary: 62C07 , 62C15
Secondary: 62F03

Keywords: data-splitting , inadmissible test , Moran’s single-split test , regular admissibility

Vol.16 • No. 1 • 2022
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