MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS
We consider statistics of the form T = Sigma(n)(j=1) xi(j)f(j) + R, where xi(j), f(j,) j = 1, ..., n, and R are M-measurable random variables for some sigma-algebra M. Assume that there exist sigma-algebras M-(1), ..., M-(n), M-(j) subset of M, j = 1, ..., n, such that E(xi(j) vertical bar M-(j)) = 0. Under these assumptions, we prove an inequality for E vertical bar T vertical bar(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.
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Siam Publications