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

Kuang‐Fu ‐F Cheng

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)113-119
Number of pages7
JournalCanadian Journal of Statistics
Volume10
Issue number2
DOIs
Publication statusPublished - 1982
Externally publishedYes

Fingerprint

Jackknife
Normal Approximation
Cumulative distribution function
Asymptotic Variance
Order Statistics
Theorem
Linear Function
Estimate
Asymptotic variance
Order statistics
Approximation
Distribution function

Keywords

  • Berry‐Esséen rate
  • Jackknife
  • L‐estimate

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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

In: Canadian Journal of Statistics, Vol. 10, No. 2, 1982, p. 113-119.

Research output: Contribution to journalArticle

Cheng, Kuang‐Fu ‐F. / On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate. In: Canadian Journal of Statistics. 1982 ; Vol. 10, No. 2. pp. 113-119.
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