Some asymptotic inferential problems connected with complex elliptical distribution
The first author [ibid. 27, 319-333 (1988; Zbl 0659.62034)] proved an asymptotic normality of the location parameters of the generalized linear growth curve model when a set of independent observations are taken from an elliptical distribution and obtained an asymptotic confidence region on the location parameters, the asymptotic distribution of the canonical correlations and an asymptotic confidence region on the discriminatory value for the linear discriminant function. In this paper, the authors extend the above-mentioned results to complex elliptical variates. To write more precisely, let \(Z=(z_ 1,z_ 2,...,z_ n)\) be n independent observations on the complex vector and consider the linear growth curve model \(Z=B\xi A^*+\epsilon\), where \(\xi\) is an unknown parameter, A and B are complex matrices of full rank and \(\epsilon_ i\) are i.i.d. column vectors with complex elliptical distribution. The authors, among others, derive the asymptotic joint distribution of \[ Z A(A^*A)^{-1}\text{ and } n^{-1}(ZZ^*- ZA(A^*A)^{-1}\Lambda^*Z^*) \] and asymptotic confidence bounds on the elements of \(\xi\) when \(\Sigma =b_ 1^{-1}E \epsilon_ i\epsilon^*_ i\) is unknown.
scientific article; zbMATH DE number 4192875