(Received July 7, 1997; revised February 9, 1998)
Abstract. Let X=A1/2G be a scale mixture of a multivariate normal distribution with X, G \in Rn, G is a multivariate normal vector, and A is a positive random variable independent of the multivariate random vector G. This study presents asymptotic results of the conditional variance-covariance, Cov(X2 | X1), X1 \in Rm, m < n, under some moment expressions. A new representation form is also presented for conditional expectation of the scale variable on the random vector X1 \in Rm, m < n. Both the asymptotic expression and the representation are manageable and in computable form. Finally, an example is presented to illustrate how the computations are carried out.
Key words and phrases: Heteroscedasticity, orthogonal polynomials, Laguerre polynomials, Laplace transform.
Source ( TeX )