Asymptotic expaxsioxs for the joint distribution of cirrelated hotellings t2 statlstics under normality
Titel:
Asymptotic expaxsioxs for the joint distribution of cirrelated hotellings t2 statlstics under normality
Auteur:
Fujikoshi, Yasunori Seo, Takashi
Verschenen in:
Communications in statistics
Paginering:
Jaargang 28 (1999) nr. 3-4 pagina's 773-788
Jaar:
1999
Inhoud:
Let T2i=z'iS-1zi, i==,…k be correlated Hotelling's T2 statistics under normality. where z=(z'i,…,z'k)' and nS are independently distributed as Nkp((O,ρ⊗∑) and Wishart distribution Wp(∑, n), respectively. The purpose of this paper is to study the distribution function F(x1,…,xk) of (T2i,…,T2k) when n is large. First we derive an asymptotic expansion of the characteristic function of (T2i,…,T2k) up to the order n-2. Next we give asymptotic expansions for (T2i,…,T2k) in two cases (i)ρ=Ik and (ii) k=2 by inverting the expanded characteristic function up to the orders n-2 and n-1, respectively. Our results can be applied to the distribution function of max (T2i,…,T2k) as a special case.
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