= Influence function of a U-statistic
{title2=$\operatorname{IF}(x;T,F)=m\{\mathbb E[h(x,X_2,\ldots,X_m)]-T(F)\}$}
For a symmetric degree-$m$ <U-statistic kernel>, the population functional is $T(F)=\int h\,dF^m$. Contaminating each of the $m$ identical distribution arguments and differentiating gives the displayed <influence function>. It equals $m$ times the first <Hoeffding projection> and gives leading <asymptotic variance> $m^2\operatorname{Var}(h_1(X))/n$. If that projection vanishes, the usual root-$n$ normal limit degenerates and higher-order projections determine the limiting law.
Back to article page
