Key points are not available for this paper at this time.
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 (Xᵢ, Xⱼ) is not assumed to be smooth.
Bickel et al. (Mon,) studied this question.