@article{ZNSL_2008_361_a2,
author = {V. A. Egorov},
title = {Two-sided estimates for the constants in {Marcinkiewicz's} inequalities},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {45--56},
year = {2008},
volume = {361},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a2/}
}
V. A. Egorov. Two-sided estimates for the constants in Marcinkiewicz's inequalities. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 45-56. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a2/
[1] A. N. Kolmogoroff, “Über die Summen durch den Zufall bestimmter unabhängiger Grössen”, Math. Ann., 99 (1928), 309–319 ; 102 (1929), 484–488 | DOI | MR | Zbl | DOI | MR | Zbl
[2] S. N. Bernshtein, Teoriya veroyatnostei, Gostekhizdat, M.–L., 1946
[3] W. Hoeffding, “Probability inequalities for sums of bounded random variables”, J. Amer. Statist. Assos., 58:301 (1963), 13–30 | DOI | MR | Zbl
[4] G. Bennet, “Probability inequalities for the sum of independent random variables”, J. Amer. Statist. Assos., 57:297 (1962), 33–45 | DOI | Zbl
[5] D. F. Fuk, S. V. Nagaev, “Veroyatnostnye neravenstva dlya summ nezavisimykh sluchainykh velichin”, Teor. veroyatn. i ee prim., 16:4 (1971), 660–675 | MR | Zbl
[6] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR
[7] V. V. Petrov, Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987 | MR
[8] V. Egorov, “On the growth rate of moments of random sums”, Publ. IRMA Lille, 44:4 (1997), 1–8
[9] V. A. Egorov, “Ob asimptoticheskom povedenii samonormirovannykh summ sluchainykh velichin”, Teor. veroyatn. i ee prim., 41:3 (1996), 643–650 | MR | Zbl
[10] V. A. Egorov, “Otsenka postoyannykh v verkhnikh neravenstvakh Martsinkevicha i Rozentalya”, Zap. nauchn. semin. POMI, 341, POMI, SPb., 2007, 115–123 | MR | Zbl
[11] V. A. Egorov, “Ob otsenke khvosta raspredeleniya normirovannykh i samonormirovannykh summ”, Zap. nauchn. semin. POMI, 294, POMI, SPb., 2002, 77–87 | MR | Zbl
[12] E. Gine, F. Götze, D. M. Mason, “When is the Student-Statistics asymptotically standard normal?”, Ann. Probab., 25:3 (1997), 1514–1531 | DOI | MR | Zbl
[13] B. Y. Jing, Q. M. Shao, Q. Wang, “Self-normalized Cramer-type large deviations for independent random values”, Ann. Probab., 31:4 (2003), 2167–2215 | DOI | MR | Zbl
[14] M. Loev, Teoriya veroyatnostei, IL, M., 1962 | MR