On the normal approximations of V- and L-statistics

Yoshihiko Maesono

doi:10.1016/0378-3758(94)90148-1

On the normal approximations of V- and L-statistics

Yoshihiko Maesono

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

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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
Pages (from-to)	291-314
Number of pages	24
Journal	Journal of Statistical Planning and Inference
Volume	42
Issue number	3
DOIs	https://doi.org/10.1016/0378-3758(94)90148-1
Publication status	Published - Dec 1994

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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title = "On the normal approximations of V- and L-statistics",

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.",

keywords = "Berry-Ess{\'e}en bound, L-statistics, Stein's method, U-statistics, V-statistics",

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AU - Maesono, Yoshihiko

PY - 1994/12

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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.

KW - Berry-Esséen bound

KW - L-statistics

KW - Stein's method

KW - U-statistics

KW - V-statistics

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

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SP - 291

EP - 314

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 3

ER -

On the normal approximations of V- and L-statistics

Abstract

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