We investigate the asymptotic laws of some estimators of the generalized association parameter and the signed symmetric covariation coefficient in an empirical study. Estimators of the generalized association parameter (g.a.p) are based on two ways of estimating the spectral measure: the empirical characteristic function and one-dimensional projections of the data. The estimator of the signed symmetric covariation coefficient (scov) is based on fractional lower-order moments (FLOM). In the case of sub-Gaussian symmetric alpha-stable random vectors, the correlation coefficient between components of the Gaussian underlying vector coincides with the generalized association parameter and, when it exists, the signed symmetric covariation coefficient. The estimator of this quantity is based on fractional lower order moments.

symmetric alpha-stable random vector, covariation, association, correlation, spectral measure.

Received: December 16, 2021; Accepted: January 22, 2022; Published: February 4, 2022

How to cite this article: Bernédy Nel Messie Kodia Banzouzi, Claude Mederic Ndimba, Lavie Phanie Moulogho Issayaba and Davy Cardorel Nzaba Kaya, An empirical study of the asymptotic laws of some estimators of generalized association parameter and signed symmetric covariation coefficient, Far East Journal of Theoretical Statistics 64 (2022), 1-44. DOI: 10.17654/0972086322001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 

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