Error bounds for asymptotic expansion of
the conditional variance of the scale mixtures of
the multivariate normal distribution

Stergios B. Fotopoulos and Lijian He

Department of Management and Systems, and the Program in Statistics,
Washington State University, Pullman, WA 99164-4726, U.S.A.

(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 )