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Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality

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  • Hwang, S.Y.
  • Basawa, I.V.
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    Abstract

    Multivariate tree-indexed Markov processes are discussed with applications. A Galton-Watson super-critical branching process is used to model the random tree-indexed process. Martingale estimating functions are used as a basic framework to discuss asymptotic properties and optimality of estimators and tests. The limit distributions of the estimators turn out to be mixtures of normals rather than normal. Also, the non-null limit distributions of standard test statistics such as Wald, Rao's score, and likelihood ratio statistics are shown to have mixtures of non-central chi-square distributions. The models discussed in this paper belong to the local asymptotic mixed normal family. Consequently, non-standard limit results are obtained.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 6 (July)
    Pages: 1018-1031

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:1018-1031

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    Keywords: Branching-Markov process Martingale estimating functions LAMN (local asymptotic mixed normality) Large sample tests Asymptotic optimality;

    References

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    1. 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.
    2. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
    3. Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    4. Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, 09.
    5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:
    1. 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.
    2. Hwang, S.Y., 2013. "Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 127-134.

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