Rocky Mountain Journal of Mathematics

Complete convergence for weighted sums of $\rho^*$-mixing random fields

Mi-Hwa Ko

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we generalize the complete convergence for $\rho^*$-mixing random fields given by Kuczmaszewska et al.~\cite{kuclag} to the case of weight sums.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1595-1605.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1420071555

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1595

Mathematical Reviews number (MathSciNet)
MR3295643

Zentralblatt MATH identifier
1335.60038

Subjects
Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems

Keywords
Strong law of large numbers convergence rates $\rho^*$-mixing random field weighted sums

Citation

Ko, Mi-Hwa. Complete convergence for weighted sums of $\rho^*$-mixing random fields. Rocky Mountain J. Math. 44 (2014), no. 5, 1595--1605. doi:10.1216/RMJ-2014-44-5-1595. https://projecteuclid.org/euclid.rmjm/1420071555


Export citation

References

  • R.C. Bradley, On the spectral density and asymptotic normality of weakly dependent random fields, J. Theor. Prob. 5 (1992), 355–373.
  • ––––, Equivalent mixing conditions for random fields, Ann. Prob. 21 (1993), 1921–1926.
  • W. Bryc and W. Smolenski, Moment conditions for almost sure convergence of weakly correlated random variables, Proc. Amer. Math. Soc. 119 (1993), 629–635.
  • W.T. Gu, G.G. Roussas and L.T. Tran, On the convergence rate fixed design regression estimators for negatively associated random variables, Statist. Prob. Lett. 77 (2007), 1214–1224.
  • D. Kafles and M. Bhaskara Rao, Weak consistency of least squares estimators in linear models, J. Multivar. Anal. 12 (1982), 186–198.
  • A. Kuczmaszewska, On complete convergence for arrays of rowwise negatively associated random variables, Statist. Prob. Lett. 79 (2009), 116–124.
  • A. Kuczmaszewska and Z.A. Lagodowski, Convergence rates in the SLLN for some classes of dependent random field, J. Math. Anal. Appl. 380 (2011), 571–584.
  • C. Miller, Three theorems of $\rho^*$-mixing random fields, J. Theor. Prob. 7 (1994), 867–882.
  • M. Peligrad, Maximum of partial sums and an invariance principle for a class of weakly dependent random variables, Proc. Amer. Math. Soc. 126 (1998), 1181–1189.
  • M. Peligrad and A. Gut, Almost sure results for class of dependent random variables, J. Theor. Prob. 12 (1999), 87–104.
  • M.B. Priestley and M.T. Chao, Nonparametric function fitting, J. Roy. Stat. Soc. 34 (1972), 385–392.
  • C.R. Rao and M.T. Chao, Linear representation of M-estimates in linear models, Canad. J. Statist. 20 (1992), 359–368.