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Normal approximation for quasi-associated random fields

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  • Bulinski, Alexander
  • Suquet, Charles

Abstract

For quasi-associated random fields (comprising negatively and positively dependent fields) on we use Stein's method to establish the rate of normal approximation for partial sums taken over arbitrary finite subsets of .

Suggested Citation

  • Bulinski, Alexander & Suquet, Charles, 2001. "Normal approximation for quasi-associated random fields," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 215-226, September.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:2:p:215-226
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    References listed on IDEAS

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    1. Peligard, Magda & Suresh, Ram, 1995. "Estimation of variance of partial sums of an associated sequence of random variables," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 307-319, April.
    2. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    3. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    4. Bradley, Richard C. & Bryc, Wlodzimierz, 1985. "Multilinear forms and measures of dependence between random variables," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 335-367, June.
    5. Pruss, Alexander R. & Szynal, Dominik, 2000. "On the central limit theorem for negatively correlated random variables with negatively correlated squares," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 299-309, June.
    6. Shao, Qi-Man & Su, Chun, 1999. "The law of the iterated logarithm for negatively associated random variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 139-148, September.
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    Cited by:

    1. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    2. Hamri Mohamed Mehdi & Dib Abdassamad & Rabhi Abbes, 2022. "Asymptotic Properties of the Estimator of the Conditional Distribution for Associated Functional Data," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(3), pages 21-34, September.
    3. Hamza Daoudi & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2023. "Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data," Mathematics, MDPI, vol. 11(20), pages 1-24, October.
    4. Alessio Sancetta, 2009. "Strong law of large numbers for pairwise positive quadrant dependent random variables," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 55-64, February.
    5. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    6. Shashkin, Alexey, 2008. "A strong invariance principle for positively or negatively associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2121-2129, October.

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