IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i1d10.1007_s00362-024-01647-w.html
   My bibliography  Save this article

EM estimation of the B-spline copula with penalized pseudo-likelihood functions

Author

Listed:
  • Xiaoling Dou

    (Japan Women’s University
    The Institute of Statistical Mathematics)

  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

  • Gwo Dong Lin

    (Academia Sinica)

  • Donald Richards

    (Pennsylvania State University)

Abstract

The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped absolute deviation (SCAD) penalty function for the penalization term. We conduct simulation studies to demonstrate the stability of the proposed numerical procedure, show that penalization yields estimates with smaller mean-square errors when the true parameter matrix is sparse, and provide methods for determining tuning parameters and for model selection. We analyze as an example a data set consisting of birth and death rates from 237 countries, available at the website, “Our World in Data,” and we estimate the marginal density and distribution functions of those rates together with all parameters of our B-spline copula model.

Suggested Citation

  • Xiaoling Dou & Satoshi Kuriki & Gwo Dong Lin & Donald Richards, 2025. "EM estimation of the B-spline copula with penalized pseudo-likelihood functions," Statistical Papers, Springer, vol. 66(1), pages 1-34, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01647-w
    DOI: 10.1007/s00362-024-01647-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-024-01647-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-024-01647-w?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. Göran Kauermann & Christian Schellhase & David Ruppert, 2013. "Flexible Copula Density Estimation with Penalized Hierarchical B-splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 685-705, December.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Zongwu Cai & Xian Wang, 2014. "Selection of Mixed Copula Model via Penalized Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 788-801, June.
    4. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    5. Shen, Xiaojing & Zhu, Yunmin & Song, Lixin, 2008. "Linear B-spline copulas with applications to nonparametric estimation of copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3806-3819, March.
    6. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2016. "The Empirical Beta Copula," LIDAM Discussion Papers ISBA 2016032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    8. Xiaoling Dou & Satoshi Kuriki & Gwo Dong Lin & Donald Richards, 2021. "Dependence Properties of B-Spline Copulas," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 283-311, February.
    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. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    2. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    3. Zongwu Cai & Guannan Liu & Wei Long & Xuelong Luo, 2024. "Semiparametric Conditional Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202401, University of Kansas, Department of Economics, revised Jan 2024.
    4. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    5. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    6. repec:kan:wpaper:202105 is not listed on IDEAS
    7. Göran Kauermann & Christian Schellhase & David Ruppert, 2013. "Flexible Copula Density Estimation with Penalized Hierarchical B-splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 685-705, December.
    8. Nadja Klein & Thomas Kneib & Giampiero Marra & Rosalba Radice & Slawa Rokicki & Mark E. McGovern, 2018. "Mixed Binary-Continuous Copula Regression Models with Application to Adverse Birth Outcomes," CHaRMS Working Papers 18-06, Centre for HeAlth Research at the Management School (CHaRMS).
    9. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    10. Yang Li & Fan Wang & Ye Shen & Yichen Qin & Jiesheng Si, 2022. "Selection of mixed copula for association modeling with tied observations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1127-1180, December.
    11. Masuhr Andreas & Trede Mark, 2020. "Bayesian estimation of generalized partition of unity copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 119-131, January.
    12. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.
    13. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    14. Masuhr Andreas & Trede Mark, 2020. "Bayesian estimation of generalized partition of unity copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 119-131, January.
    15. Yang, Bingduo & Cai, Zongwu & Hafner, Christian M. & Liu, Guannan, 2018. "Trending Mixture Copula Models with Copula Selection," IRTG 1792 Discussion Papers 2018-057, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Xiaoling Dou & Satoshi Kuriki & Gwo Dong Lin & Donald Richards, 2021. "Dependence Properties of B-Spline Copulas," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 283-311, February.
    17. Mirza Nazmul Hasan & Roel Braekers, 2022. "Modelling the association in bivariate survival data by using a Bernstein copula," Computational Statistics, Springer, vol. 37(2), pages 781-815, April.
    18. Okhrin, Ostap & Ristig, Alexander & Sheen, Jeffrey R. & Trück, Stefan, 2015. "Conditional systemic risk with penalized copula," SFB 649 Discussion Papers 2015-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Guo, Nan & Wang, Fang & Yang, Jingping, 2017. "Remarks on composite Bernstein copula and its application to credit risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 38-48.
    20. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    21. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.

    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:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01647-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.