<p>We study the estimation of the Hellinger correlation proposed recently by Geenens and Lafaye de Micheaux (J Am Stat Assoc 117:639–653, 2022), where they show that the Hellinger correlation can be stated as a function of the integral of square-rooted copula density, and they propose a consistent estimator via the power function of a density function. In this paper, we propose a new estimator of the Hellinger correlation. We use the kernel method to estimate the copula density and then construct the estimator from the Hellinger distance. We consider both the classic kernel method and the beta kernel approach in the density estimation. The asymptotic theory has been established. Simulation results show that our kernel-based resampling estimator has performs similarly to the estimator proposed by Geenens and Lafaye de Micheaux (J Am Stat Assoc 117:639–653, 2022). Finally, we apply the estimators to a real data set to demonstrate the association between cancer mortality risk and body mass or adult life expectancy.</p>

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Kernel Copula Density Estimation of Hellinger Correlation

  • Wenjing Liu,
  • Zhi Liu

摘要

We study the estimation of the Hellinger correlation proposed recently by Geenens and Lafaye de Micheaux (J Am Stat Assoc 117:639–653, 2022), where they show that the Hellinger correlation can be stated as a function of the integral of square-rooted copula density, and they propose a consistent estimator via the power function of a density function. In this paper, we propose a new estimator of the Hellinger correlation. We use the kernel method to estimate the copula density and then construct the estimator from the Hellinger distance. We consider both the classic kernel method and the beta kernel approach in the density estimation. The asymptotic theory has been established. Simulation results show that our kernel-based resampling estimator has performs similarly to the estimator proposed by Geenens and Lafaye de Micheaux (J Am Stat Assoc 117:639–653, 2022). Finally, we apply the estimators to a real data set to demonstrate the association between cancer mortality risk and body mass or adult life expectancy.