IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v195y2023ics0167715222002772.html
   My bibliography  Save this article

Laplace’s method and BIC model selection for least absolute value criterion

Author

Listed:
  • Bardet, Jean-Marc

Abstract

In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in log(n) remains the same in the context of a selection of explanatory variables by least absolute value regression.

Suggested Citation

  • Bardet, Jean-Marc, 2023. "Laplace’s method and BIC model selection for least absolute value criterion," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715222002772
    DOI: 10.1016/j.spl.2022.109764
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002772
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109764?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.
    2. Richard A. Davis & William T. M. Dunsmuir, 1997. "Least Absolute Deviation Estimation for Regression with ARMA Errors," Journal of Theoretical Probability, Springer, vol. 10(2), pages 481-497, April.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(3), pages 403-436, June.
    5. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    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. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    2. Tae-Hwan Kim & Halbert White, 2003. "Estimation, Inference, And Specification Testing For Possibly Misspecified Quantile Regression," Advances in Econometrics, in: Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later, pages 107-132, Emerald Group Publishing Limited.
    3. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    4. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    5. Uribe, Jorge M. & Chuliá, Helena & Guillén, Montserrat, 2017. "Uncertainty, systemic shocks and the global banking sector: Has the crisis modified their relationship?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 50(C), pages 52-68.
    6. Cho, Jin Seo & Kim, Tae-hwan & Shin, Yongcheol, 2015. "Quantile cointegration in the autoregressive distributed-lag modeling framework," Journal of Econometrics, Elsevier, vol. 188(1), pages 281-300.
    7. Marilena Furno, 2012. "Tests for structural break in quantile regressions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(4), pages 493-515, October.
    8. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    9. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    10. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    11. Marilena Furno, 2008. "Quantile regressions analysis of the Italian school system," Working Papers 2008-06, Universita' di Cassino, Dipartimento di Economia e Giurisprudenza.
    12. Chaohua Dong & Jiti Gao & Yundong Tu & Bin Peng, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Papers 2301.06631, arXiv.org.
    13. Furno, Marilena, 2013. "Quantile regression and structural change in the Italian wage equation," Economic Modelling, Elsevier, vol. 30(C), pages 420-434.
    14. Alexander Aue & Rex C. Y. Cheung & Thomas C. M. Lee & Ming Zhong, 2014. "Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1241-1256, September.
    15. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
    16. Tae-Hwy Lee & Aman Ullah & He Wang, 2023. "The Second-order Bias and Mean Squared Error of Quantile Regression Estimators," Working Papers 202313, University of California at Riverside, Department of Economics.
    17. Lee, Tae-Hwy & Ullah, Aman & Wang, He, 2018. "The second-order bias of quantile estimators," Economics Letters, Elsevier, vol. 173(C), pages 143-147.
    18. Li, Zheng & Zeng, Jingjing & Hensher, David A., 2023. "An efficient approach to structural breaks and the case of automobile gasoline consumption in Australia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 169(C).
    19. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    20. Chen, Mei-Yuan & Kuan, Chung-Ming, 2001. "Testing parameter constancy in models with infinite variance errors," Economics Letters, Elsevier, vol. 72(1), pages 11-18, July.

    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:eee:stapro:v:195:y:2023:i:c:s0167715222002772. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.