Edgeworth expansions of a studentized U-statistic and a jackknife estimator of variance

Yoshihiko Maesono

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n 12). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n-1) is established for the studentized U-statistic with arbitrary degree of the kernel.

Original languageEnglish
Pages (from-to)61-84
Number of pages24
JournalJournal of Statistical Planning and Inference
Volume61
Issue number1
Publication statusPublished - May 30 1997

Fingerprint

Edgeworth Expansion
Jackknife
U-statistics
Statistics
Error term
Estimator
kernel
Decomposition
Decompose
Arbitrary
Approximation
Edgeworth expansion

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Edgeworth expansions of a studentized U-statistic and a jackknife estimator of variance. / Maesono, Yoshihiko.

In: Journal of Statistical Planning and Inference, Vol. 61, No. 1, 30.05.1997, p. 61-84.

Research output: Contribution to journalArticle

@article{8c99aff72a704a34a8722d71cb5214a9,
title = "Edgeworth expansions of a studentized U-statistic and a jackknife estimator of variance",
abstract = "We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n 12). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n-1) is established for the studentized U-statistic with arbitrary degree of the kernel.",
author = "Yoshihiko Maesono",
year = "1997",
month = "5",
day = "30",
language = "English",
volume = "61",
pages = "61--84",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Edgeworth expansions of a studentized U-statistic and a jackknife estimator of variance

AU - Maesono, Yoshihiko

PY - 1997/5/30

Y1 - 1997/5/30

N2 - We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n 12). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n-1) is established for the studentized U-statistic with arbitrary degree of the kernel.

AB - We obtain the H-decomposition of a jackknife estimator of the variance of U-statistic and derive an Edgeworth expansion with remainder term o(n 12). We also obtain an approximation of a studentized U-statistic substituting the jackknife estimator of the variance. An Edgeworth expansion with remainder term o(n-1) is established for the studentized U-statistic with arbitrary degree of the kernel.

UR - http://www.scopus.com/inward/record.url?scp=0031591328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031591328&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031591328

VL - 61

SP - 61

EP - 84

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1

ER -