Asymptotic normality of a modified estimator of Gini distance correlation

Yongli Sang () and Xin Dang
Additional contact information
Yongli Sang: University of Louisiana at Lafayette
Xin Dang: University of Mississippi

Statistical Papers, 2024, vol. 65, issue 8, No 2, 4843-4860

Abstract: 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.

Keywords: Asymptotic normality; K-sample test; Modified Gini distance correlation; Reproducing kernel Hilbert space; 62G35; 62G20 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-024-01575-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01575-9

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-024-01575-9

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().