On the almost sure central limit theorem for associated random variables

• Autorzy: Matula P.
• Języki publikacji: EN

Abstrakty

EN

The aim of this note is to prove the strong version of the CLT for associated sequences without any strong approximation theorems. In the proofs we only apply the weighted convergence result for averages of associated random variables and the standard CLT.

Słowa kluczowe

EN

central limit theorem; CLT; associated sequences; strong approximation theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 2
• Strony: 411--416
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Matula P.

• Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

Bibliografia

• [1] I. Berkes and H. Dehling, On the almost sure central limit theorem for random variables with infinite variance, J. Theoret. Probab. 7 (1994), pp. 667-680.
• [2] Т. Вirkel, Momentenabschätzungen und Grenzwertsätze für Partialsummen assoziierter Zufallsvariablen, Doctor Thesis, 1986.
• [3] — Moment bounds for associated sequences, Ann. Probab. 16 (1988), pp. 1184-1193.
• [4] —On the convergence rate in the central limit theorem for associated random variables, ibidem 16 (1988), pp. 1685-1698.
• [5] — The invariance principle for associated processes, Stochastic Process. Appl. 27 (1988), pp. 57-71.
• [6] J. Esary, F. Proschan and D. Walkup, Association of random variables with applications, Ann. Math. Statist. 38 (1967), pp. 1466-1474.
• [7] L. Horvath and D. Khoshnevisan, A strong approximation for logarithmic averages, Studia Sci. Math. Hungar. 31 (1996), pp. 187-196.
• [8] G. Hurelbaatar, On the almost sure central limit theorem for Ф-mixing random variables, ibidem 31 (1996), pp. 197-202.
• [9] M. T. Lacey and W. Philipp, A note on the almost sure central limit theorem, Statist. . Probab. Lett. 9 (1990), pp. 201-205.
• [10] P. Matula, Convergence of weighted averages of associated random variables, Probab. Math. Statist 16 (1996), pp. 337-343.
• [11] M. Peligrad and Q-M. Shao, A note on the almost sure central limit theorem for weakly dependent random variables, Statist. Probab. Lett. 22 (1995), pp. 131-136.
• [12] B. Rodzik and Z. Rychlik, On the central limit theorem for independent random variables with almost sure convergence, Probab. Math. Statist. 16 (1996), pp. 299-309.
• [13] P. Schatte, On the strong version of the central limit theorem, Math. Nachr. 137 (1988), pp. '249-256.