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A note on P-spline additive models with correlated errors

Author

Listed:
  • Maria Durbán

    (Universidad Carlos III de Madrid)

  • Iain D. Currie

    (Heriot-Watt University)

Abstract

Summary We consider additive models with k smooth terms and correlated errors, and use the penalised spline approach of Eilers & Marx (1996) to estimate the smooth functions. We obtain explicit expressions for the hat-matrix of the model and each individual curve. P-splines are represented as mixed models and REML is used to select the smoothing and correlation parameters. The method is applied to the analysis of some time series data.

Suggested Citation

  • Maria Durbán & Iain D. Currie, 2003. "A note on P-spline additive models with correlated errors," Computational Statistics, Springer, vol. 18(2), pages 251-262, July.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:2:d:10.1007_s001800300143
    DOI: 10.1007/s001800300143
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    References listed on IDEAS

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    1. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    2. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    3. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    4. Michael Smith & Chi‐Ming Wong & Robert Kohn, 1998. "Additive nonparametric regression with autocorrelated errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 311-331.
    5. Harris, John L. & Liu, Lon-Mu, 1993. "Dynamic structural analysis and forecasting of residential electricity consumption," International Journal of Forecasting, Elsevier, vol. 9(4), pages 437-455, December.
    6. Brent A. Coull & David Ruppert & M. P. Wand, 2001. "Simple Incorporation of Interactions into Additive Models," Biometrics, The International Biometric Society, vol. 57(2), pages 539-545, June.
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    Cited by:

    1. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    2. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1286-1296, December.
    3. Zanin, Luca & Marra, Giampiero, 2012. "Assessing the functional relationship between CO2 emissions and economic development using an additive mixed model approach," Economic Modelling, Elsevier, vol. 29(4), pages 1328-1337.
    4. Lee, Dae-Jin & Durbán, María, 2012. "Seasonal modulation mixed models for time series forecasting," DES - Working Papers. Statistics and Econometrics. WS ws122519, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Lee, Dae-Jin & Durbán, María, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," DES - Working Papers. Statistics and Econometrics. WS ws093312, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Gressani, Oswaldo & Lambert, Philippe, 2020. "The Laplace-P-spline methodology for fast approximate Bayesian inference in additive partial linear models," LIDAM Discussion Papers ISBA 2020020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Michael Wegener & Göran Kauermann, 2008. "Examining heterogeneity in implied equity risk premium using penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 35-56, February.
    8. Göran Kauermann & Timo Teuber & Peter Flaschel, 2012. "Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 409-427, April.
    9. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.

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