IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v69y2015i4p510-540.html
   My bibliography  Save this article

Estimating the Kullback–Liebler risk based on multifold cross-validation

Author

Listed:
  • Paolo Vidoni

Abstract

type="main" xml:id="stan12070-abs-0001"> This paper concerns a class of model selection criteria based on cross-validation techniques and estimative predictive densities. Both the simple or leave-one-out and the multifold or leave-m-out cross-validation procedures are considered. These cross-validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.

Suggested Citation

  • Paolo Vidoni, 2015. "Estimating the Kullback–Liebler risk based on multifold cross-validation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 510-540, November.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:510-540
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/stan.12070
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    2. Hirokazu Yanagihara & Hironori Fujisawa, 2012. "Iterative Bias Correction of the Cross‐Validation Criterion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 116-130, March.
    3. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    4. Yasunori Fujikoshi & Takafumi Noguchi & Megu Ohtaki & Hirokazu Yanagihara, 2003. "Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 537-553, September.
    5. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2006. "Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1965-1975, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter Beckert, 2015. "Choice in the Presence of Experts," Birkbeck Working Papers in Economics and Finance 1503, Birkbeck, Department of Economics, Mathematics & Statistics.
    2. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    3. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    4. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    5. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    6. Blasques, Francisco & van Brummelen, Janneke & Gorgi, Paolo & Koopman, Siem Jan, 2024. "Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    8. Hommes, Cars & Zhu, Mei, 2014. "Behavioral learning equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 778-814.
    9. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    10. Eric Hillebrand & Marcelo C. Medeiros, 2016. "Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-41, January.
    11. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    12. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    13. Filipe, Sara Ferreira & Grammatikos, Theoharry & Michala, Dimitra, 2016. "Forecasting distress in European SME portfolios," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 112-135.
    14. Wang, Xuexin, 2015. "A Note on Consistent Conditional Moment Tests," MPRA Paper 69005, University Library of Munich, Germany.
    15. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    16. Bodnar, Taras & Hautsch, Nikolaus, 2012. "Copula-based dynamic conditional correlation multiplicative error processes," SFB 649 Discussion Papers 2012-044, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Kuper, Gerard H. & Lestano, 2007. "Dynamic conditional correlation analysis of financial market interdependence: An application to Thailand and Indonesia," Journal of Asian Economics, Elsevier, vol. 18(4), pages 670-684, August.
    18. Ericsson, Jan & Huang, Xiao & Mazzotta, Stefano, 2016. "Leverage and asymmetric volatility: The firm-level evidence," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 1-21.
    19. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    20. Chen, Li-Ching & Wang, Jiun-Yi, 2013. "Testing the fit of the logistic model for matched case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 309-319.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:510-540. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.