IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2015-031.html
   My bibliography  Save this paper

Simultaneous likelihood-based bootstrap confidence sets for a large number of models

Author

Listed:
  • Zhilova, Mayya

Abstract

The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity. Theoretical results state the bootstrap validity in the following setting: the sample size n is fixed, the maximal parameter dimension p_max and the number of considered parametric models K are s.t. (log?K )^12 p_max^3/n is small. We also consider the situation when the parametric models are misspecified. If the models' misspecification is significant, then the bootstrap critical values exceed the true ones and the simultaneous bootstrap confidence set becomes conservative. Numerical experiments for local constant and local quadratic regressions illustrate the theoretical results.

Suggested Citation

  • Zhilova, Mayya, 2015. "Simultaneous likelihood-based bootstrap confidence sets for a large number of models," SFB 649 Discussion Papers 2015-031, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2015-031
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/122000/1/831849967.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Spokoiny, Vladimir & Zhilova, Mayya, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers 2014-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    3. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    4. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    5. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    6. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    7. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Klochkov, Yegor & Härdle, Wolfgang Karl & Xu, Xiu, 2019. "Localizing Multivariate CAViaR," IRTG 1792 Discussion Papers 2019-007, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Dzemski, Andreas & Okui, Ryo, 2018. "Confidence Set for Group Membership," Working Papers in Economics 727, University of Gothenburg, Department of Economics.
    3. Andreas Dzemski & Ryo Okui, 2024. "Confidence set for group membership," Quantitative Economics, Econometric Society, vol. 15(2), pages 245-277, May.

    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. repec:hum:wpaper:sfb649dp2015-031 is not listed on IDEAS
    2. Alexandre Belloni & Mingli Chen & Victor Chernozhukov, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk," Papers 1607.00286, arXiv.org, revised Oct 2019.
    3. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    4. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    5. Tang, Yanlin & Song, Xinyuan & Zhu, Zhongyi, 2015. "Threshold effect test in censored quantile regression," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 149-156.
    6. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    7. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    8. 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.
    9. Belloni, Alexandre & Chen, Mingli & Chernozhukov, Victor, 2016. "Quantile Graphical Models : Prediction and Conditional Independence with Applications to Financial Risk Management," Economic Research Papers 269321, University of Warwick - Department of Economics.
    10. Zeng, Zijian & Li, Meng, 2021. "Bayesian median autoregression for robust time series forecasting," International Journal of Forecasting, Elsevier, vol. 37(2), pages 1000-1010.
    11. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    12. repec:wyi:journl:002112 is not listed on IDEAS
    13. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(5), pages 941-968, October.
    14. Das, Priyam & Ghosal, Subhashis, 2018. "Bayesian non-parametric simultaneous quantile regression for complete and grid data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 172-186.
    15. 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.
    16. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    17. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    18. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. He, Yaoyao & Zheng, Yaya, 2018. "Short-term power load probability density forecasting based on Yeo-Johnson transformation quantile regression and Gaussian kernel function," Energy, Elsevier, vol. 154(C), pages 143-156.
    20. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Asongu, Simplice A. & Odhiambo, Nicholas M., 2021. "Inequality, finance and renewable energy consumption in Sub-Saharan Africa," Renewable Energy, Elsevier, vol. 165(P1), pages 678-688.
    22. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.

    More about this item

    Keywords

    simultaneous inference; correction for multiplicity; family-wise error; misspecified model; multiplier/weighted bootstrap GARCH; identification via heteroskedasticity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:zbw:sfb649:sfb649dp2015-031. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.