## Abstract

Suppose that a statistician observes two independent variates X_{1} and X_{2} having densities f_{i} (·; θ) ≡ f_{i} (·−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 X_{2} in order to conduct a one-sided test in the direction of X_{1}. Specifically, if b_{1} and b_{2} are the (1 − α)’th and α’th quantiles associated with the distribution of X_{2} under H, then Moran’s test has a rejection zone (a, ∞) × (b_{1}, ∞) ∪(−∞,a) × (−∞,b_{2}) 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 f_{1}(·) andf_{2}(·) under which Moran’s test is inadmissible.

Original language | English |
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Pages (from-to) | 3036-3059 |

Number of pages | 24 |

Journal | Electronic Journal of Statistics |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - 2022 |

Externally published | Yes |

## Keywords

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