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Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models

  • Panagiotelis, Anastasios
  • Smith, Michael

In this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions. Each function is written as a linear combination of basis terms, with coefficients regularized by a proper linearly constrained Gaussian prior. Given any potentially rank deficient prior precision matrix, we show how to derive linear constraints so that the corresponding effect is identified in the additive model. This allows for the use of a wide range of bases and precision matrices in priors for regularization. By introducing indicator variables, each constrained Gaussian prior is augmented with a point mass at zero, thus allowing for function selection. Posterior inference is calculated using Markov chain Monte Carlo and the smoothness in the functions is both the result of shrinkage through the constrained Gaussian prior and model averaging. We show how using non-degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case. We show the favourable performance of our approach when compared to two contemporary alternative Bayesian methods. To highlight the potential of our approach in high-dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra-day electricity load. Both models feature a variety of different univariate and bivariate functions which require different levels of smoothing, and where component selection is meaningful. Priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 143 (2008)
Issue (Month): 2 (April)
Pages: 291-316

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Handle: RePEc:eee:econom:v:143:y:2008:i:2:p:291-316
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Koop, Gary M & Poirier, Dale J & Tobias, Justin, 2005. "Semiparametric Bayesian Inference in Multiple Equation Models," Staff General Research Papers 12009, Iowa State University, Department of Economics.
  2. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
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  7. Alexandre Pintore & Paul Speckman & Chris C. Holmes, 2006. "Spatially adaptive smoothing splines," Biometrika, Biometrika Trust, vol. 93(1), pages 113-125, March.
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  9. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
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  11. Koop, G. & Poirier, D., 2000. "Bayesian Variants of Some Classical Semiparametric Regression Techniques," Papers 00-01-22, California Irvine - School of Social Sciences.
  12. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
  13. Chib, Siddhartha & Jeliazkov, Ivan, 2006. "Inference in Semiparametric Dynamic Models for Binary Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 685-700, June.
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  15. Smith, M. & Yau, P. & Shively, T. & Kohn, R., 1998. "Estimating Long-Term Trends in Tropospheric Ozone Levels," Monash Econometrics and Business Statistics Working Papers 2/98, Monash University, Department of Econometrics and Business Statistics.
  16. Patrick J. Wolfe & Simon J. Godsill & Wee-Jing Ng, 2004. "Bayesian variable selection and regularization for time-frequency surface estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 575-589.
  17. Ramanathan, Ramu & Engle, Robert & Granger, Clive W. J. & Vahid-Araghi, Farshid & Brace, Casey, 1997. "Shorte-run forecasts of electricity loads and peaks," International Journal of Forecasting, Elsevier, vol. 13(2), pages 161-174, June.
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