On the Correlation Coefficient of a Bivariate, Equal Variance, Complex Gaussian Sample

Berger, Toby

Berger, Toby

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 2000-2003 / Harvested from Project Euclid

Résumé

Let $u_n$ denote the sample correlation coefficient for $n$ observations from a bivariate, equal variance, complex Gaussian distribution. In this note we derive the exact distribution of $u_n$ by extending a method of Mehta and Gurland to the complex case. The asymptotic behavior of $E|u_n|^k$ as $n \rightarrow \infty$ is determined via the method of steepest descent. Applicability of the results to the analysis of certain estimators of spectral parameters of stationary time series is discussed.

Publié le : 1972-12-14
Classification:

@article{1177690873,
     author = {Berger, Toby},
     title = {On the Correlation Coefficient of a Bivariate, Equal Variance, Complex Gaussian Sample},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 2000-2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177690873}
}

Berger, Toby. On the Correlation Coefficient of a Bivariate, Equal Variance, Complex Gaussian Sample. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  2000-2003. http://gdmltest.u-ga.fr/item/1177690873/