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

Kuang‐Fu ‐F Cheng

doi:10.2307/3314903

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

Kuang‐Fu ‐F Cheng

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 V²_n be the jackknife estimate of the asymptotic variance of n ^1/2T(F_n) or n ^1/2T*(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	https://doi.org/10.2307/3314903
Publication status	Published - Jun 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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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 V2n 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‐Ess{\'e}en 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.",

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PY - 1982/6

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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 V2n 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 V2n 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

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KW - L‐estimate

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

Abstract

Keywords

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