The Edgeworth Expansion for $U$-Statistics of Degree Two
P. J. Bickel, F. Gotze, W. R. van Zwet
The Annals of Statistics · 1986 · Volume 14 · Issue 4
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.
Keywords
$U$-statistics, 60F05, 62E20, Edgeworth expansion, second order asymptotics
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