The Edgeworth Expansion for $U$-Statistics of Degree Two

P. J. Bickel; F. Gotze; W. R. van Zwet

doi:10.1214/aos/1176350170

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December, 1986 The Edgeworth Expansion for $U$-Statistics of Degree Two

P. J. Bickel, F. Gotze, W. R. van Zwet

Ann. Statist. 14(4): 1463-1484 (December, 1986). DOI: 10.1214/aos/1176350170

Abstract

An Edgeworth expansion with remainder $o(N^{-1})$ is established for a $U$-statistic with a kernel $h$ of degree 2. The assumptions involved appear to be very mild; in particular, the common distribution of the summands $h(X_i, X_j)$ is not assumed to be smooth.

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P. J. Bickel. F. Gotze. W. R. van Zwet. "The Edgeworth Expansion for $U$-Statistics of Degree Two." Ann. Statist. 14 (4) 1463 - 1484, December, 1986. https://doi.org/10.1214/aos/1176350170