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1995•JOURNAL OF THE JAPAN STATISTICAL SOCIETYOpen access

ON THE NORMAL APPROXIMATIONS OF STUDENTIZED U-STATISTIC

Yoshihiko Maesono

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Abstract

The rates of convergence to a normal distribution and an Edgeworth expansion are investigated for a studentized U-statistic with arbitrary degree. In this paper we obtain an Edgeworth expansion with remainder term o(n-1/2) and prove the validity of the expansion. We also derive an inequality which gives a lower bound of the uniform distance between two distributions of the studentized U-statistic and normal.

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The rates of convergence to a normal distribution and an Edgeworth expansion are investigated for a studentized U-statistic with arbitrary degree. In this paper we obtain an Edgeworth expansion with remainder term o(n-1/2) and prove the validity of the expansion. We also derive an inequality which gives a lower bound of the uniform distance between two distributions of the studentized U-statistic and normal.

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Available abstract

The rates of convergence to a normal distribution and an Edgeworth expansion are investigated for a studentized U-statistic with arbitrary degree. In this paper we obtain an Edgeworth expansion with remainder term o(n-1/2) and prove the validity of the expansion. We also derive an inequality which gives a lower bound of the uniform distance between two distributions of the studentized U-statistic and normal.

Key concepts: Studentized range, Edgeworth series, Statistic, Mathematics, Remainder, Normal distribution, Statistics, Term (time)

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