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This paper is concerned with error bounds for asymptotic expansions of the distribution of a multivariate scale mixture variate defined by X 1⁄4 SZ, where Z 1⁄4 ðZ1; . . . ;ZpÞ 0, Z1; . . . ;Zp are i:i:d: random variables, and S is a symmetric positive definite random matrix independent of Z. Recently Fujikoshi, Ulyanov and Shimizu (2005) obtained L1-norm error bounds for asymptotic expansions of the density function of X when S 1⁄4 diagðS1; . . . ;SpÞ. In this paper, first we obtain uniform error bounds for asymptotic expansions of the distribution function of X under the same diagonal structure of S. Next we extend the L1-norm error bounds to tha case when S is a symmetric positive definite random matrix provided Z1 is distributed as the standard normal distribution Nð0; 1Þ.

Error bounds for asymptotic expansions of the distribution of multivariate scale mixture