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The asymptotic behaviors for least square estimation of multi-casting autoregressive processes

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  • Mao, Mingzhi

Abstract

This paper mainly discusses the asymptotic properties of multi-casting autoregressive processes. By using the m-dependence of random vectors, we prove that the least squares (LS) estimator of the unknown parameters satisfies the moderate deviation principle. Two examples of regular cases are also presented.

Suggested Citation

  • Mao, Mingzhi, 2014. "The asymptotic behaviors for least square estimation of multi-casting autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 110-124.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:110-124
    DOI: 10.1016/j.jmva.2014.04.014
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    References listed on IDEAS

    as
    1. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    2. de Saporta, Benoîte & Gégout-Petit, Anne & Marsalle, Laurence, 2012. "Asymmetry tests for bifurcating auto-regressive processes with missing data," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1439-1444.
    3. Hwang, S.Y. & Choi, M.S., 2009. "Modeling and large sample estimation for multi-casting autoregression," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1943-1950, September.
    4. Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
    5. Hwang, S.Y. & Basawa, I.V., 2009. "Branching Markov processes and related asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1155-1167, July.
    6. Mas, André & Menneteau, Ludovic, 2003. "Large and moderate deviations for infinite-dimensional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 241-260, November.
    Full references (including those not matched with items on IDEAS)

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