We give a short proof of the Jackknife Estimate of Variance of Efron-Stein using martingale difference techniques. The method could be used to get information on other moments than the second moment.

Let [phi] be a convex function defined on R+, with [phi](0) = 0 and limx--0[phi](x)/x=0. We show that there exists a uniformly bounded process (Xt) on [0,1] with continuous sample paths that satisfies the increment condition for every u t, E([phi]( Xt- Xu)) [less-than-or-equals, slant] t - u....