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Degrees of freedom and model selection in semiparametric additive monotone regression

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  • Rueda, Cristina

Abstract

The degrees of freedom of semiparametric additive monotone models are derived using results about projections onto sums of order cones. Two important related questions are also studied, namely, the definition of estimators for the parameter of the error term and the formulation of specific Akaike Information Criteria statistics. Several alternatives are proposed to solve both problems and simulation experiments are conducted to compare the behavior of the different candidates. A new selection criterion is proposed that combines the ability to guess the model but also the efficiency to estimate the variance parameter. Finally, the criterion is used to select the model in a regression problem from a well known data set.

Suggested Citation

  • Rueda, Cristina, 2013. "Degrees of freedom and model selection in semiparametric additive monotone regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 88-99.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:88-99
    DOI: 10.1016/j.jmva.2013.02.001
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    References listed on IDEAS

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    1. Zhao, Lincheng & Peng, Limin, 2002. "Model selection under order restriction," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 301-306, May.
    2. Borra, Simone & Di Ciaccio, Agostino, 2002. "Improving nonparametric regression methods by bagging and boosting," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 407-420, February.
    3. Sampson, Allan R. & Singh, Harshinder & Whitaker, Lyn R., 2003. "Order restricted estimators: some bias results," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 299-308, February.
    4. Xiao Ni & Daowen Zhang & Hao Helen Zhang, 2010. "Variable Selection for Semiparametric Mixed Models in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 79-88, March.
    5. Cristina Rueda & José Menéndez & Federico Gómez, 2010. "Small area estimators based on restricted mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 558-579, November.
    6. Kato, Kengo, 2009. "On the degrees of freedom in shrinkage estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1338-1352, August.
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    Cited by:

    1. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    2. Cristina Rueda & Miguel A. Fernández & Sandra Barragán & Kanti V. Mardia & Shyamal D. Peddada, 2016. "Circular piecewise regression with applications to cell‐cycle data," Biometrics, The International Biometric Society, vol. 72(4), pages 1266-1274, December.
    3. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    4. María José Lombardía & Esther López-Vizcaíno & Cristina Rueda, 2021. "Selection model for domains across time: application to labour force survey by economic activities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 228-254, March.

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