### 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 | |

Publication status | Published - Jan 1 1991 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Planning and Inference*,

*27*(1), 37-50. https://doi.org/10.1016/0378-3758(91)90080-X

**On the normal approximation of U-statistics of degree two.** / Maesono, Yoshihiko.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 27, no. 1, pp. 37-50. https://doi.org/10.1016/0378-3758(91)90080-X

}

TY - JOUR

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

AU - Maesono, Yoshihiko

PY - 1991/1/1

Y1 - 1991/1/1

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 - http://www.scopus.com/inward/record.url?scp=0040627537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040627537&partnerID=8YFLogxK

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

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

M3 - Article

VL - 27

SP - 37

EP - 50

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1

ER -