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Likelihood-free Bayesian estimation of multivariate quantile distributions

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  • Drovandi, Christopher C.
  • Pettitt, Anthony N.
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    Abstract

    In this paper, we present new multivariate quantile distributions and utilise likelihood-free Bayesian algorithms for inferring the parameters. In particular, we apply a sequential Monte Carlo (SMC) algorithm that is adaptive in nature and requires very little tuning compared with other approximate Bayesian computation algorithms. Furthermore, we present a framework for the development of multivariate quantile distributions based on a copula. We consider bivariate and time series extensions of the g-and-k distribution under this framework, and develop an efficient component-wise updating scheme free of likelihood functions to be used within the SMC algorithm. In addition, we trial the set of octiles as summary statistics as well as functions of these that form robust measures of location, scale, skewness and kurtosis. We show that these modifications lead to reasonably precise inferences that are more closely comparable to computationally intensive likelihood-based inference. We apply the quantile distributions and algorithms to simulated data and an example involving daily exchange rate returns.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311001125
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 9 (September)
    Pages: 2541-2556

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2541-2556

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Approximate Bayesian computation Copula g-and-k distribution Multivariate Quantile distributions Sequential Monte Carlo;

    References

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    1. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    2. Christopher C. Drovandi & Anthony N. Pettitt & Malcolm J. Faddy, 2011. "Approximate Bayesian computation using indirect inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(3), pages 317-337, 05.
    3. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-72, October.
    4. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
    5. Matthias Fischer, 2010. "Generalized Tukey-type distributions with application to financial and teletraffic data," Statistical Papers, Springer, vol. 51(1), pages 41-56, January.
    6. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436.
    7. Knut Heggland & Arnoldo Frigessi, 2004. "Estimating functions in indirect inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 447-462.
    8. J. M�ller & A. N. Pettitt & R. Reeves & K. K. Berthelsen, 2006. "An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants," Biometrika, Biometrika Trust, vol. 93(2), pages 451-458, June.
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    Cited by:
    1. Menéndez, P. & Fan, Y. & Garthwaite, P.H. & Sisson, S.A., 2014. "Simultaneous adjustment of bias and coverage probabilities for confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 35-44.
    2. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.

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