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Bayesian Curve Estimation By Model Averaging

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  • Daniel Peña

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  • M. Dolores Redondas

    ()

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    Abstract

    A bayesian approach is used to estimate a nonparametric regression model. The main features of the procedure are, first, the functional form of the curve is approximated by a mixture of local polynomials by Bayesian Model Averaging (BMA); second, the model weights are approximated by the BIC criterion, and third, a robust estimation procedure is incorporated to improve the smoothness of the estimated curve. The models considered at each sample points are polynomial regression models of order smaller that four, and the parameters of each model are estimated by a local window. The estimated value is computed by BMA, and the posterior probability of each model is approximated by the exponential of the BIC criterion. The robustness is achieved by assuming that the noise follows a scale contaminated normal model so that the effect of possible outliers is downweighted. The procedure provides a smooth curve and allows a straightforward prediction and quantification of the uncertainty. The method is illustrated with several examples and some Monte Carlo experiments.

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws034410.

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    Date of creation: Sep 2003
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    Handle: RePEc:cte:wsrepe:ws034410

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    1. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
    2. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
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