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A note on predictive densities based on composite likelihood methods

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  • Paolo Vidoni

    (University of Udine)

Abstract

Whenever the computation of data distribution is unfeasible or inconvenient, the classical predictive procedures prove not to be useful. These rely, after all, on the conditional distribution of the future random variable, which is also unavailable. This paper considers a notion of composite likelihood for specifying composite predictive distributions, viewed as surrogates for true unknown predictive distribution. In particular, the focus is on the pairwise likelihood obtained as a weighted product of likelihood factors related to bivariate events associated with both the sample data and future observation. The specification of the weights, and more generally the evaluation of the frequentist properties of alternative pairwise predictive distributions, is performed by considering the mean square prediction error of the associated predictors and the expected Kullback–Liebler loss of the related predictive densities. Finally, simple examples concerning autoregressive models are presented.

Suggested Citation

  • Paolo Vidoni, 2018. "A note on predictive densities based on composite likelihood methods," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 31-48, April.
    • Handle: RePEc:spr:metron:v:76:y:2018:i:1:d:10.1007_s40300-017-0118-y
    DOI: 10.1007/s40300-017-0118-y
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    References listed on IDEAS

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    1. Richard E. Chandler & Steven Bate, 2007. "Inference for clustered data using the independence loglikelihood," Biometrika, Biometrika Trust, vol. 94(1), pages 167-183.
    2. Cristiano Varin & Paolo Vidoni, 2009. "Pairwise Likelihood Inference for General State Space Models," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 170-185.
    3. Masao Ueki & Kaoru Fueda, 2007. "Adjusting estimative prediction limits," Biometrika, Biometrika Trust, vol. 94(2), pages 509-511.
    4. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    5. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    6. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    7. Varin, Cristiano & Vidoni, Paolo, 2006. "Pairwise likelihood inference for ordinal categorical time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2365-2373, December.
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    Cited by:

    1. Wagner Barreto‐Souza & Hernando Ombao, 2022. "The negative binomial process: A tractable model with composite likelihood‐based inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 568-592, June.

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