## Abstract

The order of the increase in the Fisher information measure contained in a finite number k of additive statistics or sample quantiles, constructed from a sample of size n, as n → ∞, is investigated. It is shown that the Fisher information in additive statistics increases asymptotically in a manner linear with respect to n, if 2 + δ moments of additive statistics exist for some δ > 0. If this condition does not hold, the order of increase in this information is non-linear and the information may even decrease. The problem of asymptotic sufficiency of sample quantiles is investigated and some linear analogues of maximum likelihood equations are constructed. AMS classifications: Primary 62B10, 62E20, 62F10, 62F12.

Original language | English |
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Pages (from-to) | 93-108 |

Number of pages | 16 |

Journal | Journal of Statistical Planning and Inference |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jun 1996 |

## Keywords

- Additive statistics
- Asymptotic sufficiency
- Estimation
- Fisher information measure
- Sample quantiles

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics