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On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria

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  • Guyon, Xavier
  • Yao, Jian-feng

Abstract

For a general class of order selection criteria, we establish analytic and non-asymptotic evaluations of both the underfitting and overfitting sets of selected models. These evaluations are further specified in various situations including regressions and autoregressions with finite or infinite variances. We also show how upper bounds for the misfitting probabilities and hence conditions ensuring the weak consistency can be derived from the given evaluations. Moreover, it is demonstrated how these evaluations, combined with a law of the iterated logarithm for some relevant statistic, can provide conditions ensuring the strong consistency of the model selection criterion used.

Suggested Citation

  • Guyon, Xavier & Yao, Jian-feng, 1999. "On the Underfitting and Overfitting Sets of Models Chosen by Order Selection Criteria," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 221-249, August.
  • Handle: RePEc:eee:jmvana:v:70:y:1999:i:2:p:221-249
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    References listed on IDEAS

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    1. Hannan, E. J., 1981. "Estimating the dimension of a linear system," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 459-473, December.
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    3. Geweke, John & Meese, Richard, 1981. "Estimating regression models of finite but unknown order," Journal of Econometrics, Elsevier, vol. 16(1), pages 162-162, May.
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    6. Bai, Z. D. & Subramanyam, K. & Zhao, L. C., 1988. "On determination of the order of an autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 40-52, October.
    7. Pötscher, B.M., 1991. "Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models," Econometric Theory, Cambridge University Press, vol. 7(4), pages 435-449, December.
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    Cited by:

    1. Verzelen, Nicolas, 2010. "Data-driven neighborhood selection of a Gaussian field," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1355-1371, May.
    2. Giovanna Jona Lasinio & Francesco Lagona, 2002. "Selection of the neighborhood structure for space-time Markov random field models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 293-311, October.
    3. Lee, Yoonseok & Phillips, Peter C.B., 2015. "Model selection in the presence of incidental parameters," Journal of Econometrics, Elsevier, vol. 188(2), pages 474-489.
    4. Killick, Rebecca & Eckley, Idris A., 2014. "changepoint: An R Package for Changepoint Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i03).
    5. Antoine Chambaz & Judith Rousseau, 2005. "Nonasymptotic Bounds for Bayesian Order Identification with Application to Mixtures," Working Papers 2005-27, Center for Research in Economics and Statistics.
    6. Zheng Yuan & Debashis Ghosh, 2008. "Combining Multiple Biomarker Models in Logistic Regression," Biometrics, The International Biometric Society, vol. 64(2), pages 431-439, June.
    7. Lv, Qichao & Rashidi-Khaniabadi, Ali & Zheng, Rong & Zhou, Tongke & Mohammadi, Mohammad-Reza & Hemmati-Sarapardeh, Abdolhossein, 2023. "Modelling CO2 diffusion coefficient in heavy crude oils and bitumen using extreme gradient boosting and Gaussian process regression," Energy, Elsevier, vol. 275(C).
    8. Xavier Guyon & Cécile Hardouin, 2014. "Misparametrization subsets for penalized least squares model selection," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 283-294, October.

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