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Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process

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  • Claudio Macci
  • Stefano Trapani

Abstract

We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. Normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the rate function can be expressed in terms of the divergence between two spectral densities. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Claudio Macci & Stefano Trapani, 2013. "Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 703-719, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:703-719
    DOI: 10.1007/s10463-012-0389-2
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    References listed on IDEAS

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    1. Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, January.
    2. 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.
    3. Claudio Macci, 2010. "Large deviations for estimators of some threshold parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 63-77, March.
    4. James Fu & Robert Kass, 1988. "The exponential rates of convergence of posterior distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 683-691, December.
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