ABSTRACT
I S*(r:J.) (''U*)(U*)d -z K-I"'K E ("U*) 2 d 'hl*-w 1ere 1; fJ = 0 11 li li '· T11 = L.-i=l ** a11 li , an Wit 1111 = sup{ID"H(Xn + x)l: llxll::; IIX;,- Xnll, lo:l S.i}, .i 2:: I, the remainder term Qi11 admits the bound
Next,recallthefactthatforsquarematricesB1andB2,ifB2isnonsingular andIIB1-B2 11·IIB2 1II<1/2,thenB! 1existsandIIB1 1II<2IIB2 1II·Sinceon At,,
fornlarge,itfollowsthatq;~: 1E**S(/1,L1)S(/1,L;)')- 1existsanditsnorm isboundedaboveby211~~11/n.Therefore,byLemma4.1,onthesetAj11 ,
~C(d,11~~1 11,EIIZxll 4 )(np)- 1(logn)- 2•(5.7)
and
(5.8)
(5.9)
(5.11)
Next we further simplify the second term by replacing a11 with a. Note that if X 1, . .. , X11 are such that !IX11 - 11·11 < C(d, II L:x II )n-112 (1og n) 112 , then on the set A~~~
