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

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概要

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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 $\vX=\vS \vZ$, where $\vZ=(Z_1,\cdots,Z_p)', Z_1,\ldots, Z_p$ are $i.i.d.$ random variables, and $\vS$ is a symmetric positive definite random matrix independent of $\vZ$. Recently Fujikoshi, Ulyanov and Shimizu (2005) obtained $L_1$-norm error bounds for asymptotic expansions of the density function of $\vX$ when $\vS=\diag(S_1, \ldots, S_p)$. In this paper, first we obtain uniform error bounds for asymptotic expansions of the distribution function of $\vX$ under the same diagonal structure of $\vS$. Next we extend the $L_1$-norm error bounds to tha case when $\vS$ is a symmetric positive definite random matrix provided $Z_1$ is distributed as the standard normal distribution $N(0, 1)$.

• 広島大学の論文

著者

• Fujikoshi Yasunori

  Department of Mathematics, Hiroshima University

• Ulyanov Vladimir

  Department Of Mathematical And Cybernetics Faculty Of Computational Mathematics And Cybernetics Mosc

• Ulyanov Vladimir

  Department Of Mathematical Statistics Faculty Of Computational Mathematics And Cybernetics Moscow St

• Shimizu Ryoichi

  The Institute of Statistical Mathematics

• Fujikoshi Yasunori

  Department Of Mathematics Graduate School Of Science Hiroshima University

• Fujikoshi Yasunori

  Department Of Mathematics Faculty Of Science Hiroshima University

関連論文

• A HETEROGENEITY TEST STATISTIC OF K CANONICAL CORRELATIONS AND ITS APPLICATION TO PRENATAL EXPOSURE
• Error bounds for asymptotic expansions of the distribution of multivariate scale mixture
• Refinement on the convergence of one family of goodness-of-fit statistics to chi-squared distribution
• STABILITY OF MULTIDIMENSIONAL SCALING WITH AN ERROR MODEL

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