MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS

Götze F, Naumov AA, Tikhomirov AN (2020)
THEORY OF PROBABILITY AND ITS APPLICATIONS 65(1): 1-16.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Götze, FriedrichUniBi; Naumov, A. A.; Tikhomirov, A. N.
Abstract / Bemerkung
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.
Stichworte
statistics of independent random variables; Rosenthal's inequality; U-statistics; Wigner's semicircle law; Stieltjes transform; moment; inequalities
Erscheinungsjahr
2020
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
65
Ausgabe
1
Seite(n)
1-16
ISSN
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2945466

Zitieren

Götze F, Naumov AA, Tikhomirov AN. MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2020;65(1):1-16.
Götze, F., Naumov, A. A., & Tikhomirov, A. N. (2020). MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS. THEORY OF PROBABILITY AND ITS APPLICATIONS, 65(1), 1-16. doi:10.1137/S0040585X97T989787
Götze, F., Naumov, A. A., and Tikhomirov, A. N. (2020). MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS. THEORY OF PROBABILITY AND ITS APPLICATIONS 65, 1-16.
Götze, F., Naumov, A.A., & Tikhomirov, A.N., 2020. MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS. THEORY OF PROBABILITY AND ITS APPLICATIONS, 65(1), p 1-16.
F. Götze, A.A. Naumov, and A.N. Tikhomirov, “MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 65, 2020, pp. 1-16.
Götze, F., Naumov, A.A., Tikhomirov, A.N.: MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS. THEORY OF PROBABILITY AND ITS APPLICATIONS. 65, 1-16 (2020).
Götze, Friedrich, Naumov, A. A., and Tikhomirov, A. N. “MOMENT INEQUALITIES FOR LINEAR AND NONLINEAR STATISTICS”. THEORY OF PROBABILITY AND ITS APPLICATIONS 65.1 (2020): 1-16.

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