Convergence rates in the law of large numbers for arrays

• Autorzy: Kruglov V. , Volodina A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present new sufficient conditions for complete convergence for sums of arrays of rowwise independent random variables. These conditions appear to be necessary and sufficient in the case of partial sums of independent identically distributed random variables. Many known results on complete convergence can be obtained as corollaries to theorems proved in this paper.

Słowa kluczowe

EN

arrays of rowwise independent random variables; complete convergence; rate of convergence; law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 1
• Strony: 63--76
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kruglov V.

• Department of Mathematical Statistics, Faculty of Applied Mathematics and Cybernetics, Moscow State University, Vorob’evy Gory 119899, Moscow, Russia

autor

Volodina A.

• Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S0A2 Canada

Bibliografia

• [1] Z. Bai and Ch. Su, The complete convergence for partial sums of iid random variables, Scientia Sinica. Series A, 28 (1985), pp. 1261-1277.
• [2] К. B. Baum and M. Katz, Convergence rates in the law of large numbers, Trans. Amer. Math. Soc. 120 (1965), pp. 108-123.
• [3] P. Erdos, On a theorem of Hsu and Robbins, Ann. Math, Statist. 20 (1949), pp. 286-291.
• [4] P. Erdos, Remark on my paper “On a theorem of Hsu and Robbins'’, Ann. Math. Statist. 21 (1950), p. 138.
• [5] A. Gut, On complete convergence in the law of large numbers for subsequences, Ann. Probab. 13 (1985), pp. 1286-1291.
• [6] A. Gut, Complete convergence for arrays, Period. Math. Hungar. 25 (1992), pp. 51-75.
• [7] P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Natl. Acad. Sei. USA 33 (1947), pp. 25-31.
• [8] T. C. Hu, F. Moricz and R. L. Taylor, Strong law of large numbers for arrays of rowwise independent random variables, Acta Math. Acad. Sei. Hungar. 54 (1989), pp. 153-162.
• [9] V. M. Kruglov, A. Volodin and T.-C. Hu, On complete convergence for arrays, Statist. Probab. Lett. 76 (2006), pp. 1631-1640.
• [10] M. Loève, Probability Theory I, Springer, 1977.
• [11] M. Maejima, A theorem on convergence for weighted sums of i.i.d. random variables, Rep. Statist Appl. Res. Un. Japan. Sci. Engrs. 24 (1977), pp. 1-4.
• [12] F. L. Spitzer, A combinatorial lemma and its applications, Trans. Amer. Math. Soc. 82 (1956), pp. 323-339.