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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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    Cited by:

    1. 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.
    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. Wen, Kuangyu & Wu, Ximing, 2017. "Smoothed kernel conditional density estimation," Economics Letters, Elsevier, vol. 152(C), pages 112-116.

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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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