Simple sufficient condition for inadmissibility of Moran’s single-split test

Royi Jacobovic*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Suppose that a statistician observes two independent variates X1 and X2 having densities fi (·; θ) ≡ fi (·−θ),i=1, 2, θ ∈ R. His purpose is to conduct a test for H: θ =0 vs. K: θ ∈ R \{0} 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 (1 − α)’th and α’th quantiles associated with the distribution of X2 under H, then Moran’s test has a rejection zone (a, ∞) × (b1, ∞) ∪(−∞,a) × (−∞,b2) where a ∈ R 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(·) andf2(·) under which Moran’s test is inadmissible.

Original languageEnglish
Pages (from-to)3036-3059
Number of pages24
JournalElectronic Journal of Statistics
Issue number1
StatePublished - 2022
Externally publishedYes


  • Moran’s single-split test
  • data-splitting
  • inadmissible test
  • regular admissibility


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