J. Japan Statist. Soc., Vol. 33 (No. 1), pp. 77-94, 2003

Edgeworth Expansions of Some Statistics Including the LB-Statistic and V-Statistic

Hajime Yamato, Toshifumi Nomachi and Koichiro Toda

Abstract. As an estimator of an estimable parameter, Toda and Yamato (2001) introduced a linear combination Yn of U-statistics which includes V-statistic and LB-statistic. We give the Edgeworth expansions of the standardized Yn statistic with remainder o(n-1) in case that the kernel is not degenerate. We also give the Edgeworth expansions of the studentized Yn statistic using a jackknife variance estimator with remainder o(n-1/2).

Key words and phrases: Edgeworth expansion, linear combination of U-statistics, V-statistic.

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