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Asymptotic normality of a modified estimator of Gini distance correlation

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  • Yongli Sang

    (University of Louisiana at Lafayette)

  • Xin Dang

    (University of Mississippi)

Abstract

Recently, the Gini distance correlation (GDC), $$\rho _g$$ ρ g , was proposed to measure dependence between numerical and categorical variables (Dang et al. 2021). This new dependence measure can mutually characterize independence between the random variables. That is, $$\rho _g=0$$ ρ g = 0 if and only only the categorical variable and the numerical variable are independent. Limiting distributions of the naive estimator of GDC have been established in Dang et al. (2021). It has been shown that under independence, the empirical GDC admits a degenerating limit which is an infinite weighted sum of Chi-squared distributions. In this paper, we propose a modified estimator of the GDC that is asymptotically normal under independence between the numerical and the categorical variables. We also extend this method to the generalized GDC Zhang et al. (2019) in reproducing kernel Hilbert space (RKHS). Both the modified GDC and generalized GDC can be applied to test the K-sample problem. Simulations studies are conducted to examine the finite sample performance of the new K-sample test based on the modified estimators.

Suggested Citation

  • Yongli Sang & Xin Dang, 2024. "Asymptotic normality of a modified estimator of Gini distance correlation," Statistical Papers, Springer, vol. 65(8), pages 4843-4860, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01575-9
    DOI: 10.1007/s00362-024-01575-9
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    References listed on IDEAS

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    1. Makigusa, Natsumi & Naito, Kanta, 2020. "Asymptotic normality of a consistent estimator of maximum mean discrepancy in Hilbert space," Statistics & Probability Letters, Elsevier, vol. 156(C).
    2. Balogoun, Armando Sosthène Kali & Nkiet, Guy Martial & Ogouyandjou, Carlos, 2021. "Asymptotic normality of a generalized maximum mean discrepancy estimator," Statistics & Probability Letters, Elsevier, vol. 169(C).
    3. Xin Dang & Dao Nguyen & Yixin Chen & Junying Zhang, 2021. "A new Gini correlation between quantitative and qualitative variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1314-1343, December.
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