### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Berry‐Esséen rate
- Jackknife
- L‐estimate

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Canadian Journal of Statistics*,

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

**On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate.** / Cheng, Kuang‐Fu ‐F.

Research output: Contribution to journal › Article

*Canadian Journal of Statistics*, vol. 10, no. 2, pp. 113-119. https://doi.org/10.2307/3314903

}

TY - JOUR

T1 - On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate

AU - Cheng, Kuang‐Fu ‐F

PY - 1982

Y1 - 1982

N2 - Consider a linear function of order statistics (“L‐estimate”) which can be expressed as a statistical function T(Fn) based on the sample cumulative distribution function Fn. Let T*(Fn) be the corresponding jackknifed version of T(Fn), and let V2 n be the jackknife estimate of the asymptotic variance of n 1/2T(Fn) or n 1/2T*(Fn). In this paper, we provide a Berry‐Esséen rate of the normal approximation for a Studentized jackknife L‐estimate n1/2[T*(Fn) ‐ T(F)]/Vn, where T(F) is the basic functional associated with the L‐estimate.

AB - Consider a linear function of order statistics (“L‐estimate”) which can be expressed as a statistical function T(Fn) based on the sample cumulative distribution function Fn. Let T*(Fn) be the corresponding jackknifed version of T(Fn), and let V2 n be the jackknife estimate of the asymptotic variance of n 1/2T(Fn) or n 1/2T*(Fn). In this paper, we provide a Berry‐Esséen rate of the normal approximation for a Studentized jackknife L‐estimate n1/2[T*(Fn) ‐ T(F)]/Vn, where T(F) is the basic functional associated with the L‐estimate.

KW - Berry‐Esséen rate

KW - Jackknife

KW - L‐estimate

UR - http://www.scopus.com/inward/record.url?scp=84988087261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988087261&partnerID=8YFLogxK

U2 - 10.2307/3314903

DO - 10.2307/3314903

M3 - Article

AN - SCOPUS:84988087261

VL - 10

SP - 113

EP - 119

JO - Canadian Journal of Statistics

JF - Canadian Journal of Statistics

SN - 0319-5724

IS - 2

ER -