Mots-clés : concentration, orthogonal polynomials.
@article{TVP_2003_48_4_a5,
author = {S. G. Bobkov and F. G\"otze},
title = {On the central limit theorem along subsequences of noncorrelated observations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {745--765},
year = {2003},
volume = {48},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a5/}
}
S. G. Bobkov; F. Götze. On the central limit theorem along subsequences of noncorrelated observations. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 745-765. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a5/
[1] Anttila M., Ball K., Perissinaki I., “The central limit problem for convex bodies”, Trans. Amer. Math. Soc., 355:12 (2003), 4723–4735 | DOI | MR | Zbl
[2] Bentkus V., Götze F., “The Berry–Esseen bound for Student's statistic”, Ann. Probab., 24:1 (1996), 491–503 | DOI | MR | Zbl
[3] Bobkov S. G., “On concentration of distributions of random weighted sums”, Ann. Probab., 31:1 (2003), 195–215 | DOI | MR | Zbl
[4] Bobkov S. G., “Concentration of distributions of the weighted sums with Bernoullian coefficients”, Lecture Notes in Math., 1807, 2003, 27–36 | MR | Zbl
[5] Bobkov S. G., Götze F., “Exponential integrability and transportation cost related to logarithmic Sobolev inequalities”, J. Funct. Anal., 163:1 (1999), 1–28 | DOI | MR | Zbl
[6] Chistyakov G., Götze F., “Limit distributions of studentized means”, Ann. Probab. (to appear) | MR
[7] Diaconis P., Freedman D., “Asymptotics of graphical projection pursuit”, Ann. Statist., 12:3 (1984), 793–815 | DOI | MR | Zbl
[8] Giné E., Götze F., Mason D. M., “When is the Student $t$-statistic asymptotically standard normal?”, Ann. Probab., 25:3 (1997), 1514–1531 | DOI | MR | Zbl
[9] Griffin P. S., Mason D. M., “On the asymptotic normality of self-normalized sums”, Proc. Cambridge Philos. Soc., 109:3 (1991), 597–610 | DOI | MR | Zbl
[10] Janson S., “Some pairwise independent sequences for which the central limit theorem fails”, Stochastics, 23:4 (1988), 439–448 | MR | Zbl
[11] Ledoux M., “Concentration of measure and logarithmic Sobolev inequalities”, Lecture Notes in Math., 1709, 1999, 120–216 | MR | Zbl
[12] Logan B., Mallows C., Rice S., Shepp L., “Limit distributions of self-normalized sums”, Ann. Probab., 1 (1973), 788–809 | DOI | MR | Zbl
[13] Maller R. A., “A theorem on products of random variables, with application to regression”, Austral. J. Statist., 23:2 (1981), 177–185 | DOI | MR | Zbl
[14] Meier P.-A., Veroyatnost i potentsialy, Mir, M., 1973, 334 pp.
[15] Pruss A. R., “A bounded $N$-tuplewise independent and identically distributed counterexample to the CLT”, Probab. Theory Related Fields, 111:3 (1998), 323–332 | DOI | MR | Zbl
[16] Shao Q.-M., “Self-normalized large deviations”, Ann. Probab., 25:1 (1997), 285–328 | DOI | MR | Zbl
[17] Sudakov V. N., “Tipichnye raspredeleniya lineinykh funktsionalov v konechnomernykh prostranstvakh vysokoi razmernosti”, Dokl. AN SSSR, 243:6 (1978), 1578–1582 | MR | Zbl
[18] Wang Q., Jing B.-Y., “An exponential nonuniform Berry–Esseen bound for self-normalized sums”, Ann. Probab., 27:4 (1999), 2068–2088 | DOI | MR | Zbl
[19] von Weizsäcker H., “Sudakov's typical marginals, random linear functionals and a conditional central limit theorem”, Probab. Theory Related Fields, 107:3 (1997), 313–324 | DOI | MR | Zbl