### Abstract

Consider the problem of estimating the mean by using a random sample from a normal population. Let (Equation presented) denote the sample mean and consider the estimator that assumes the value zero when (Equation presented) and the value (Equation presented) when (Equation presented). This is called a preliminary test estimator. For most of the usual loss functions it is inadmissible. In this article we show that for some loss functions, which include a complexity cost, the estimator is admissible. The results are related to Cohen’s work on hybrid estimation and hypothesis-testing problems. © 1979, Taylor & Francis Group, LLC.

Original language | English (US) |
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Pages (from-to) | 872-874 |

Number of pages | 3 |

Journal | Journal of the American Statistical Association |

Volume | 74 |

Issue number | 368 |

DOIs | |

State | Published - 1979 |

### Keywords

- Admissibility
- Complexity cost
- Normal mean
- Preliminary test

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## Cite this

Meeden, G., & Arnold, B. C. (1979). The admissibility of a preliminary test estimator when the loss incorporates a complexity cost.

*Journal of the American Statistical Association*,*74*(368), 872-874. https://doi.org/10.1080/01621459.1979.10481045