A strong invariance principle for negatively associated random fields

Guang-hui Cai

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 27-40
  • ISSN: 0011-4642

Abstract

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In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite ( 2 + δ ) th moment and the covariance coefficient u ( n ) exponentially decreases to 0 . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.

How to cite

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Cai, Guang-hui. "A strong invariance principle for negatively associated random fields." Czechoslovak Mathematical Journal 61.1 (2011): 27-40. <http://eudml.org/doc/196488>.

@article{Cai2011,
abstract = {In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite $(2+\delta )$th moment and the covariance coefficient $u(n)$ exponentially decreases to $0$. The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.},
author = {Cai, Guang-hui},
journal = {Czechoslovak Mathematical Journal},
keywords = {strong invariance principle; negative association; random field; blocking technique; quantile transform; strong invariance principle; negative association; random field; blocking technique; quantile transform},
language = {eng},
number = {1},
pages = {27-40},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A strong invariance principle for negatively associated random fields},
url = {http://eudml.org/doc/196488},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Cai, Guang-hui
TI - A strong invariance principle for negatively associated random fields
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 27
EP - 40
AB - In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite $(2+\delta )$th moment and the covariance coefficient $u(n)$ exponentially decreases to $0$. The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
LA - eng
KW - strong invariance principle; negative association; random field; blocking technique; quantile transform; strong invariance principle; negative association; random field; blocking technique; quantile transform
UR - http://eudml.org/doc/196488
ER -

References

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  1. Alam, K., Saxena, K. M. L., Positive dependence in multivariate distributions, Comm. Statist. A 10 1183-1196. (1981) Zbl0471.62045MR0623526
  2. Balan, R. M., 10.1214/009117904000001071, Ann. Probab. 33 823-840. (2005) Zbl1070.60032MR2123212DOI10.1214/009117904000001071
  3. Berkes, I., Philipp, W., Approximation theorems for independent and weakly dependent random vectors, Ann. Probab. 7 19-54. (1979) Zbl0392.60024MR0515811
  4. Berkes, I., Morrow, G. J., 10.1007/BF00533712, Z. Wahrsch. view. Gebiete 57 15-37. (1981) Zbl0443.60029MR0623453DOI10.1007/BF00533712
  5. Bulinski, Shashkin, The strong invariance principles for dependent multi-indexed random variables, Dokl. Acad. Nauk 403 155-158. (2005) MR2161593
  6. Bulinski, Shashkin, Strong invariance principles for dependent random fields, ISM Lect. Notes-Monograph Series Dynamics and Stochastics 48 128-143. (2006) MR2306195
  7. Cai, G. H., Wang, J. F., 10.1016/j.spl.2008.07.039, Statistics and Probability Letters 79 215-222. (2009) Zbl1157.60013MR2483543DOI10.1016/j.spl.2008.07.039
  8. Csörgő, M., Révész, P., 10.1007/BF00532865, Z. Wahrsch. view. Gebiete 31 255-260. (1975) MR0375411DOI10.1007/BF00532865
  9. Csörgő, M., Révész, P., Strong Approximations in Probability and Statistics, Academic Press, New York. (1981) MR0666546
  10. Feller, W., An Introduction to Probability Theory and its Applications 2, 2nd ed John Wiley. New York. (1971) MR0088081
  11. Joag-Dev, K., Proschan, F., 10.1214/aos/1176346079, Ann. Statist. 11 286-295. (1983) MR0684886DOI10.1214/aos/1176346079
  12. Newman, C. M., Asympotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in Statistics and Probability (Tong, Y. L., ed., Institute of Mathematical Statistics, Hayward, CA) 127-140. (1984) MR0789244
  13. Roussas, G. G., 10.1006/jmva.1994.1039, J. Multivariate Anal. 50 152-173. (1994) Zbl0806.60040MR1292613DOI10.1006/jmva.1994.1039
  14. Shao, Q. M., Su, C., 10.1016/S0304-4149(99)00026-5, Stochastic Process. Appl. 83 139-148. (1999) MR1705604DOI10.1016/S0304-4149(99)00026-5
  15. Su, C., Zhao, L., Wang, Y., 10.1007/BF02874436, Sci. China Ser. A 40 172-182. (1997) Zbl0907.60023MR1451096DOI10.1007/BF02874436
  16. Wichura, M. J., 10.1214/aop/1176996980, Ann. Probab. 1 272-296. (1973) Zbl0288.60030MR0394894DOI10.1214/aop/1176996980
  17. Yu, H., A strong invariance principle for associated sequences, Ann. Probab. 24 2079-2097. (1996) Zbl0879.60028MR1415242
  18. Zhang, L. X., 10.1023/A:1006720512467, Acta Math. Hungar. 86 237-259. (2000) Zbl0964.60035MR1756175DOI10.1023/A:1006720512467
  19. Zhang, L. X., 10.1006/jmva.2000.1949, J. Multivariate Anal. 78 272-298. (2001) Zbl0989.60033MR1859759DOI10.1006/jmva.2000.1949
  20. Zhang, L. X., Wen, J. W., 10.1016/S0167-7152(01)00021-9, Statist. Probab. Lett. 53 259-267. (2001) Zbl0994.60026MR1841627DOI10.1016/S0167-7152(01)00021-9

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