### Abstract

The rates of convergence to the normal distribution are investigated for V- and L-statistics. We derive an inequality which gives a lower bound of the uniform distance between two distributions of the V-statistic and the normal distribution. We obtain an inequality which gives a lower bound of the uniform distance, and is meaningful in the case that the distribution of the standardized V-statistic is symmetric around the origin. Further, we also derive similar inequalities for the L-statistic. The proofs are based on Stein's method.

Original language | English |
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Pages (from-to) | 291-314 |

Number of pages | 24 |

Journal | Journal of Statistical Planning and Inference |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1994 |

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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*,

*42*(3), 291-314. https://doi.org/10.1016/0378-3758(94)90148-1

**On the normal approximations of V- and L-statistics.** / Maesono, Yoshihiko.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 42, no. 3, pp. 291-314. https://doi.org/10.1016/0378-3758(94)90148-1

}

TY - JOUR

T1 - On the normal approximations of V- and L-statistics

AU - Maesono, Yoshihiko

PY - 1994/1/1

Y1 - 1994/1/1

N2 - The rates of convergence to the normal distribution are investigated for V- and L-statistics. We derive an inequality which gives a lower bound of the uniform distance between two distributions of the V-statistic and the normal distribution. We obtain an inequality which gives a lower bound of the uniform distance, and is meaningful in the case that the distribution of the standardized V-statistic is symmetric around the origin. Further, we also derive similar inequalities for the L-statistic. The proofs are based on Stein's method.

AB - The rates of convergence to the normal distribution are investigated for V- and L-statistics. We derive an inequality which gives a lower bound of the uniform distance between two distributions of the V-statistic and the normal distribution. We obtain an inequality which gives a lower bound of the uniform distance, and is meaningful in the case that the distribution of the standardized V-statistic is symmetric around the origin. Further, we also derive similar inequalities for the L-statistic. The proofs are based on Stein's method.

UR - http://www.scopus.com/inward/record.url?scp=43949158835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949158835&partnerID=8YFLogxK

U2 - 10.1016/0378-3758(94)90148-1

DO - 10.1016/0378-3758(94)90148-1

M3 - Article

VL - 42

SP - 291

EP - 314

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 3

ER -