On Berry-Esseen type bounds and asymptotic expansions for slightly trimmed means

Vestnik St. Petersburg University, Mathematics - Tập 46 Số 3 - Trang 129-142 - 2013
Nadezhda Gribkova1
1St. Petersburg State University, St. Petersburg, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

V. Bentkus, F. Götze, and W. R. van Zwet, “An Edgeworth expansion for symmetric statistics,” Ann. Statist. 25, 851–896 (1997).

N. M. Bingham, C. M. Goldie, and J. L. Teugels, “Regular variation,” in Encyclopedia Math. Appl., Vol. 27 (Cambridge Univ. Press, Cambridge, 1987).

S. Csörgö, E. Haeusler, and D. M. Mason, “The asymptotic distribution of trimmed sums,” Ann. Probab. 16, 672–699 (1988).

V. A. Egorov and V. B. Nevzorov, “Certain estimates of the rate of convergence of sums of order statistics to the normal law,” Zap. Nauch. Sem. LOMI/Leningrad. otdel. math. inst. V.A. Steklov, 1974, Vol. 41, p. 105 [128 (in Russian)]. Transl. in J. Math. Sci. (New York) 9 (1), 81–105 (1978).

W. Feller, An Introduction to Probability Theory and its Applications, II (Wiley, New York, 1967; Mir, Moscow, 1984).

N. V. Gribkova, “On analogues of Berry-Esseen inequality for truncated linear combinations of order statistics,” Theory Probab. Appl. 38(1), 142–149 (1993).

N. V. Gribkova and R. Helmers, “The empirical Edgeworth expansion for a Studentized trimmed mean,” Math. Methods Statist. 15, 61–87 (2006).

N. V. Gribkova and R. Helmers, “On the Edgeworth expansion and the M out of N bootstrap accuracy for a Studentized trimmed mean,” Math. Methods Statist. 16, 142–176 (2007).

N. V. Gribkova and R. Helmers, “On the consistency of the M ≪ N bootstrap approximation to the trimmed mean,” Theory Probab. Appl. 55(1), 42–53 (2010).

N. V. Gribkova and R. Helmers, “On a Bahadur-Kiefer representation of von Mises statistic type for intermediate sample quantiles,” Prob. Math. Statist. 32(2), 255–279 (2012).

V. Gribkova and R. Helmers, “Second-order approximation for slightly trimmed means,” Theor. Prob. Appl. 58 (2013). (in print); arXiv:1104.3347v1 [math.PR].

P. S. Griffin and W. E. Pruitt, “Asymptotic normality and subsequential limits of trimmed sums,” Ann. Probab. 17, 1186–1219 (1989).

R. Helmers, “On the Edgeworth expansion and the bootstrap approximation for a Studentized U statistic,” Ann. Statist. 19, 470–484 (1991).

W. Hoeffding, “Probability inequalities for sum of bounded random variables,” J. Amer. Statist. Assoc. 58, 13–30 (1963).

V. V. Petrov, Sums of Independent Random Variables (Nauka, Moscow, 1972; Springer, Berlin, 1975).

H. Putter and W. R. van Zwet, “Empirical Edgeworth expansions for symmetric statistics,” Ann. Statist. 26, 1540–1569 (1998).

S. M. Stigler, “The asymptotic distribution of the trimmed mean,” Ann. Statist. 1, 472–477 (1973).

W. R. van Zwet, “A Berry—Esséen bound for symmetric statistics,” Z. Wahrsch. Verw. Gebiete 66, 425–440 (1984).