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

Yoshihiko Maesono

doi:10.1016/s0378-3758(96)00148-6

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

Yoshihiko Maesono

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

7 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 language	English
Pages (from-to)	61-84
Number of pages	24
Journal	Journal of Statistical Planning and Inference
Volume	61
Issue number	1
DOIs	https://doi.org/10.1016/s0378-3758(96)00148-6
Publication status	Published - May 30 1997

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/s0378-3758(96)00148-6

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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.",

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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.

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

Abstract

All Science Journal Classification (ASJC) codes

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