On the normal approximation of U-statistics of degree two

Yoshihiko Maesono

doi:10.1016/0378-3758(91)90080-X

On the normal approximation of U-statistics of degree two

Yoshihiko Maesono

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

4 Citations (Scopus)

Abstract

The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the origin. The proof is based on Stein's method.

Original language	English
Pages (from-to)	37-50
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	27
Issue number	1
DOIs	https://doi.org/10.1016/0378-3758(91)90080-X
Publication status	Published - Jan 1991

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1016/0378-3758(91)90080-X

Cite this

@article{c984a0fe883048bfa705d6b459080ec2,

title = "On the normal approximation of U-statistics of degree two",

abstract = "The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the origin. The proof is based on Stein's method.",

author = "Yoshihiko Maesono",

year = "1991",

month = jan,

doi = "10.1016/0378-3758(91)90080-X",

language = "English",

volume = "27",

pages = "37--50",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - On the normal approximation of U-statistics of degree two

AU - Maesono, Yoshihiko

PY - 1991/1

Y1 - 1991/1

N2 - The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the origin. The proof is based on Stein's method.

AB - The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the origin. The proof is based on Stein's method.

UR - https://www.scopus.com/pages/publications/0040627537

UR - https://www.scopus.com/pages/publications/0040627537#tab=citedBy

U2 - 10.1016/0378-3758(91)90080-X

DO - 10.1016/0378-3758(91)90080-X

M3 - Article

AN - SCOPUS:0040627537

SN - 0378-3758

VL - 27

SP - 37

EP - 50

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

On the normal approximation of U-statistics of degree two

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this