Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 45, 2016 - Issue 1
Submit an article Journal homepage
247
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A central limit theorem for weighted sums of associated random field

Mi-Hwa KoDivision of Mathematics and Informational Statistics, Wonkwang University, Jeonbuk, KoreaCorrespondence[email protected]
Pages 1-8 | Received 07 Mar 2013, Accepted 10 Jun 2013, Published online: 06 Jan 2016

References

  • Billingsley, P. (1968). Convergence of Probability Measures. New York: Wiley.
  • Bulinskii, A. V. (1991). Inequalities for the moments of sums of associated multi-indexed variables. Theory Prob. Appl. 38:342–349.
  • Bulinskii, A. V., Keane, M. S. (1996). Invariance principle for associated random fields. J. Math. Sci. 81:2905–2911.
  • Cox, J. T., Grimmett, G. (1984). Central limit theorems for associated random variables and the percolation model. Ann. Prob. 12:514–528.
  • Esary, J., Proschan, F., Walkup, D. (1967). Association of random variables with applications. Ann. Math. Stat. 38:1466–1474.
  • Kafles, D., Rao, M. (1982). Weak consistency of least squares estimators in linear models. J. Multivar. Anal. 12:186–198.
  • Kim, T. S. (1996). The invariance principle for associated random fields. J. Math. 26:1443–1454.
  • Kim, T. S., Ko, M. H., Choi, Y. K. (2008). The invariance principle for linear multi-parameter stochastic processes generated by associated random fields. Statist. Prob. Lett. 78:3298–3303.
  • Ko, M. H., Kim, H. C., Kim, T. S. (2006). A central limit theorem for general weighted sums of LPQD random variables and its applications. J. Korean Math. Soc. 43:529–538.
  • Newman, C. M. (1980). Normal fluctuations and the FKG inequalities. Commun. Math. Phys. 74:119–128.
  • Peligrad, M., Utev, S. (1997). Central limit theorem for linear processes. Ann. Prob. 25:443–456.
  • Petrov, V. V. (1975). Sums of Independent Random Variables. New York: Heidelberg, Berlin.
  • Priestley, M. B., Chao, M. T. (1972). Nonparametric function fitting. J. Roy. Stat. Soc. Ser. B 34:385–392.
  • Rao, C. R., Zhao, M. T. (1992). Linear representation of M-estimates in linear models. Can. J. Stat. 20:359–368.
  • Roussas, G. (1994). Asymptotic normality of random fields of positively or negatively associated processes. J. Multivar. Anal. 50:152–173.
  • Shanskin, S. (2008). A strong invariance principle for postively or negatively associated random fields. Stat. Prob. Lett. 78:2121–2129.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.