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Penalized exponential series estimation of copula densities with an application to intergenerational dependence of body mass index

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  • Yichen Gao
  • Yu Zhang
  • Ximing Wu

Abstract

We propose a penalized maximum likelihood estimator of copula densities that is based on the multivariate exponential series density estimator. We employ an approximate likelihood cross validation method to select the smoothing parameter. We demonstrate the usefulness of the proposed method via Monte Carlo simulations. We apply this method to estimate copula densities between children’s and parents’ body mass indices (BMI). Our results suggest that the dependence relationship is generally asymmetric and stronger for females. We also find a higher intergenerational BMI dependence for low income families. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Yichen Gao & Yu Zhang & Ximing Wu, 2015. "Penalized exponential series estimation of copula densities with an application to intergenerational dependence of body mass index," Empirical Economics, Springer, vol. 48(1), pages 61-81, February.
    • Handle: RePEc:spr:empeco:v:48:y:2015:i:1:p:61-81
    DOI: 10.1007/s00181-014-0858-y
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    1. Jason Abrevaya & Hongfei Tang, 2011. "Body mass index in families: spousal correlation, endogeneity, and intergenerational transmission," Empirical Economics, Springer, vol. 41(3), pages 841-864, December.
    2. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    3. Chen, Yi-Ting, 2007. "Moment-Based Copula Tests for Financial Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 377-397, October.
    4. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    5. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen VK, 2010. "Nonparametric density estimation for multivariate bounded data," LIDAM Reprints CORE 2301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    7. Valentyn Panchenko & Artem Prokhorov, 2011. "Efficient estimation of parameters in marginals in semiparametric multivariate models," Working Papers 11001, Concordia University, Department of Economics.
    8. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
    9. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for High-Dimensional Sparse Econometric Models," Papers 1201.0220, arXiv.org.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    11. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2013. "Honest confidence regions for a regression parameter in logistic regression with a large number of controls," CeMMAP working papers 67/13, Institute for Fiscal Studies.
    12. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    14. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    15. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    16. 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.
    17. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
    18. Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
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    Cited by:

    1. Wen, Kuangyu & Wu, Ximing, 2017. "Smoothed kernel conditional density estimation," Economics Letters, Elsevier, vol. 152(C), pages 112-116.
    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. Perloff, Jeffrey M. & Schlenker, Wolfram & Sears, Molly & Wu, Ximing, 2020. "Crop Failures from Temperature and Precipitation Shocks: Implications for U.S. Crop Insurance," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304540, Agricultural and Applied Economics Association.

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    More about this item

    Keywords

    Copula; Exponential series estimator; Penalized maximum likelihood; Body mass index; C14; C30; I10;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • I10 - Health, Education, and Welfare - - Health - - - General

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