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On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate
Author(s) -
Cheng KuangFu
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314903
Subject(s) - jackknife resampling , studentized range , mathematics , combinatorics , function (biology) , delta method , statistics , standard error , biology , evolutionary biology , estimator
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.