### Abstract

The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first order efficiency, but in regular cases there is equivalence. The results are in particular applied on tests for goodness-of-fit.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1998 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1467 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-62G20
- MSC-62F05
- EWI-3287
- IR-65656
- MSC-62G10

## Cite this

Inglot, T., Kallenberg, W. C. M., & Ledwina, T. (1998).

*Vanishing shortcoming and asymptotic relative efficiency*. Enschede: University of Twente, Department of Applied Mathematics.