Error bounds for asymptotic expansions of Wilks' lambda distribution
Let [Lambda]=Se/Se+Sh, where Sh and Se are independently distributed as Wishart distributions Wp(q,[Sigma]) and Wp(n,[Sigma]), respectively. Then [Lambda] has Wilks' lambda distribution [Lambda]p,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T=-nlog[Lambda]. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms.
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Volume (Year): 97 (2006)
Issue (Month): 9 (October)
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- Fujikoshi, Y. & Ulyanov, V.V. & Shimizu, R., 2005. "L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 1-19, September.
- Ryoichi Shimizu & Yasunori Fujikoshi, 1997. "Sharp Error Bounds for Asymptotic Expansions of the Distribution Functions for Scale Mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 285-297, June.
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