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General dependence structures for some models based on exponential families with quadratic variance functions

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  • Luis Nieto-Barajas

    (ITAM)

  • Eduardo Gutiérrez-Peña

    (IIMAS-UNAM)

Abstract

We describe a procedure to introduce general dependence structures on a set of random variables. These include order-q moving average-type structures, as well as seasonal, periodic, spatial and spatio-temporal dependences. The invariant marginal distribution can be in any family that is conjugate to an exponential family with quadratic variance function. Dependence is induced via a set of suitable latent variables whose conditional distribution mirrors the sampling distribution in a Bayesian conjugate analysis of such exponential families. We obtain strict stationarity as a special case.

Suggested Citation

  • Luis Nieto-Barajas & Eduardo Gutiérrez-Peña, 2022. "General dependence structures for some models based on exponential families with quadratic variance functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 699-716, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-021-00798-4
    DOI: 10.1007/s11749-021-00798-4
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    References listed on IDEAS

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    1. Luis E. Nieto-Barajas & Peter Müller & Yuan Ji & Yiling Lu & Gordon B. Mills, 2012. "A Time-Series DDP for Functional Proteomics Profiles," Biometrics, The International Biometric Society, vol. 68(3), pages 859-868, September.
    2. E. Gutiérrez-Peña & A. Smith & José Bernardo & Guido Consonni & Piero Veronese & E. George & F. Girón & M. Martínez & G. Letac & Carl Morris, 1997. "Exponential and bayesian conjugate families: Review and extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 1-90, June.
    3. S. G. Walker, 2000. "A Note on the Innovation Distribution of a Gamma Distributed Autoregressive Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 575-576, September.
    4. M. Mendoza & L. E. Nieto‐Barajas, 2006. "Bayesian solvency analysis with autocorrelated observations," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(2), pages 169-180, March.
    5. Michael K. Pitt & Chris Chatfield & Stephen G. Walker, 2002. "Constructing First Order Stationary Autoregressive Models via Latent Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 657-663, December.
    6. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
    7. Luis E. Nieto‐Barajas & Stephen G. Walker, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 413-424, September.
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