MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS.

We consider statistics of the form T = Pn j=1 jfj +R, where j, fj, j = 1, . . ., n, and R are M-measurable random variables for some s-algebra M. Assume that there exist s-algebras M(1), . . . ,M(n), M(j) M, j = 1, . . ., n, such that E(j | M(j)) = 0. Under these assumptions, we prove an inequality for E|T|p with p > 2. We also discuss applications of the main result of the paper to estimation of moments of linear forms, U-statistics, and perturbations of the characteristic equation for the Stieltjes transform of Wigner's semicircle law. [ABSTRACT FROM AUTHOR]