Abstract
Let X= A 1/2 G be a scale mixture of a multivariate normal distribution with X, G∈ ℝn, Gis 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(X 2|X 1), X 1∈ 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 X 1∈ 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.
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Fotopoulos, S.B., He, L. Error Bounds for Asymptotic Expansion of the Conditional Variance of the Scale Mixtures of the Multivariate Normal Distribution. Annals of the Institute of Statistical Mathematics 51, 731–747 (1999). https://doi.org/10.1023/A:1004039431669
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DOI: https://doi.org/10.1023/A:1004039431669