### Abstract

Consider a linear function of order statistics (“L‐estimate”) which can be expressed as a statistical function T(F_{n}) based on the sample cumulative distribution function F_{n}. Let T*(F_{n}) be the corresponding jackknifed version of T(F_{n}), and let V^{2} _{n} be the jackknife estimate of the asymptotic variance of n ^{1/2}T(F_{n}) or n ^{1/2}T*(F_{n}). In this paper, we provide a Berry‐Esséen rate of the normal approximation for a Studentized jackknife L‐estimate n^{1/2}[T*(F_{n}) ‐ T(F)]/V_{n}, where T(F) is the basic functional associated with the L‐estimate.

Original language | English |
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Pages (from-to) | 113-119 |

Number of pages | 7 |

Journal | Canadian Journal of Statistics |

Volume | 10 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1982 |

Externally published | Yes |

### Keywords

- Berry‐Esséen rate
- Jackknife
- L‐estimate

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Cheng, KF. F. (1982). On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate.

*Canadian Journal of Statistics*,*10*(2), 113-119. https://doi.org/10.2307/3314903