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2、j)=ijiijj(i,j=1,p)ePV1/2=diag(11,pp)?IIIOOO?,K=V1/2RV1/2R=(V1/2)1(V1/2)11?!?9?O2.1?n!?5?nnn!?555?555?1?X?Y?,A,B?,KE(AX)=AE(X)E(AXB)=AE(X)BD(AX)=AD(X)A0Cov(AX,BY)=ACov(X,Y)B0.555?2eX?Y?p?,KCov(X,Y)=0,?.555?3?X=(X1,Xp)?D(X)=?K?.555?4=L2,?L?K?.AO?0?,L 01?!?9?O2.2?5?2.2?5?ooo?ddd2.2.1?U=(U1,U2,Uq)0?,U1,
3、Uq?p?N(0,1)?,?p?,A?p q?,KX=AU+?p?,X?p?,P?X Np(,AA0)555?1?U=(U1,U2,Uq)0?,U1,Uq?p?N(0,1)?,KX=AU+?A?X(t)=expit0 12t0AA0t1?!?9?O2.2?5?2.2.2ep?X?A?X(t)=expit0 12t0tKX?lp?,P?X Np(,)555?2?X Np(,),B?s p?,d?s?,-Z=BX+d,KZ Ns(B+d,BB0)5?2?5|?E?l?.?X=X(1)X(2)#rp r Np(,),?,?=(1)(2)#rp r,=11122122#rp rKX(1)Nr(1),1
4、1),X(2)Npr(2),22)1?!?9?O2.2?5?555?3eX Np(,),KE(X)=,D(X)=555?4?X=(X1,X2,Xp)0?p?,KX?lp?p?a,=a0X?C?.1?!?9?O2.2?5?2.2.3ep?X?5|?l?,KX?p?.555?5eX Np(,),?0(?),KX?f(x)=1(2)p/2|1/2exp12(x )01(x )1?!?9?O2.2?5?2.2.4ep?X?f(x)=1(2)p/2|1/2exp12(x )01(x )?p?,p?;?X?p?.1?!?9?O2.2?5?2.2.1(?)2.2.2?/9?A?p?/.1?!?9?O2.2?
5、5?1?!?9?O2.3?5?!?52.3?5?!?555nnn2.3.1ep?X Np(,)X=X(1)X(2)#Np(1)(2)#,11122122#!KX(1)?X(2)?12=0=X(1)?X(2)p?.1?!?9?O2.3?5?!?5?1?ri 0(i=1,k),?r1+r2+rk=p,kX=X(1).X(k)r1.rk Np(1).(k),111k.k1kkppKX(1),X(k)?p?ij=0(?i 6=j).?2?X=(X1,Xp)0 Np(,),e?,KX1,Xp?p?.1?!?9?O2.3?5?!?!?k?,k?,?X2?,X1?f1(x1|x2)=f(x1,x2)f2(x
6、2)?(X1|X2)N1(1+12(x2 2),21(1 2)1?!?9?O2.3?5?!?nnn2.3.2?X=X(1)X(2)#rp r Np(,)(0),K?X(2)?,X(1)?(X(1)|X(2)Nr(12,112)?12=(1)+12122(x(2)(2),112=11 1212221.1?!?9?O2.3?5?!?3n2.3.2?e?:(1)X(2)?X(1)12122X(2)?p?;(2)X(1)?X(2)21111X(1)?p?;(3)(X(2)|X(1)Npr(21,221),?21=(2)+21111(x(1)(1),221=22 2111112.1?!?9?O2.3?5
7、n!A?Vgnnn!AAA?VVVggg1.?,888XXX,?XXX?X=X(1)X(2)#Np(1)(2)#,11122122#!qfi?X(2)?,X(1)?(X(1)|X(2)Nr(12,112)12=(1)+12122(x(2)(2),?,P?E(X(1)|X(2);12?X(1)X(2)?888,12122def=B?888XXX.1?!?9?O2.3?5n!A?VgP112=(ijr+1,p)rr(i,j=1,r).rijr+1,p=ijr+1,piir+1,pjjr+1,p?X(2)=(Xr+1,Xp)0?,Xi?Xj(i,j=1,2,r)?XXX.1?!?9?O2.3?5n!
8、A?Vg2.?XXX?Z=XY#p1 Np+1 Xy#,XXXyyXyy#!,KR=yX1XXXyyy!1/2?Y?X=(X1,Xp)0?XXX.1?!?9?O2.3?5n!A?Vg3.?ZZZ?3n2.3.2?e,?r=1,PX(1)=Y,g(x(2)=E(Y|X(2),K?(),?y:E(Y g(x(2)2 E(Y (x(2)2K3?OKe,?g(x(2)Y?Z?.1?!?9?O2.4?2.4?g1?!?9?O2.5?O2.5?O?p?oNX Np(,),?X(i)=(xi1,xip)0,(i=1,n)?p?oNX?,d?*?X=x11x1p.xn1xnp1?!?9?O2.5?O?!?oN
9、?iA?!?oooNNN?iiiAAA?(1)?X:X=1nnXi=1X(i)=(x1,xp)0=1nX01n,?xi=1nnX=1xi(i=1,2,p)1?!?9?O2.5?O?!?oN?iA?(2)?l?(q?)A:A=nX=1(X()X)(X()X)0=X0X nXX0=X0In1n1n10nXdef=(aij)pp?aij=nX=1(xi xi)(xj xj)(i,j=1,2,p)1?!?9?O2.5?O?!?oN?iA?(3)?S:S=1n 1A=(sij)pp?sij=1n 1nX=1(xi xi)2(i=1,2,p)?C?Xi?;?sii?C?Xi?IIIOOO?.(4)?R:R
10、=(rij)pp,?rij=sijsiisjjor=aijaiiajj1?!?9?O2.5?O?!,?q,?O?!,?qqq,?OOO1.qqq,L(,)=nYi=11(2)p/2|1/2exp12(x(i)1(x(i)0=1(2)np/2|n/2etr121nXi=1(x(i)(x(i)0=1(2)np/2|n/2etr121(A+n(X )(X )0)1?!?9?O2.5?O?!,?q,?O2.,?kkk555?nnn2.5.1?B?p?,KtrB ln|B|p?B=Ip.1?!?9?O2.5?O?!,?q,?O3.?lnL(,)?:lnL(,)=np2ln2 n2ln|12tr1nXi=
11、1(x(i)(x(i)0=C 12tr1A+n1(X )(X )0=C 12tr(1A)n2(X )1(X )0C 12tr(1A)?“?=?=X?,=u?0,klnL(X,)=maxlnL(,)1?!?9?O2.5?O?!,?q,?OlnL(X,)=np2ln2 n2ln|12tr(1A)=np2ln2 n2ln|+tr(1An)=C1n2tr(1An)ln|1An|+ln|An|=C1n2tr(1/2An1/2)ln|1/2An1/2|+ln|An|C1np2n2+ln|An|e?B=1/2 An1/2?,d?n2.5.1?=?B=1/2 An1/2=Ip?,=An.?q,?L(X,An)
12、=(12e)np/2|A|n/21?!?9?O2.5?O?!,?q,?Onnn2.5.1?X(i)(i=1,n)?p?oNNp(,)?,n p,K,?q,?O?=X,=1nA.1?!?9?O2.5?On!?q,?O?5?nnn!?qqq,?OOO?555?nnn2.5.2?X?AO?p?oNNp(,)?l?,K1X Np(,1n)2Ad=Pn1t=1ZtZ0t,?Z1,Zn1?uNp(0,)3X?A?p?4P(A 0)=1 n p1?!?9?O2.5?On!?q,?O?5?e?q,?O?k?5?.1?52k?53?54?1?!?9?O2.5?Oo!?q,?Oooo!?qqq,?OOO?Cz?R
13、k.L()q,.?w=g()?Borel?N?,pRk?f8.?w ,-M(w)=sup:g()=wL().2.5.1M(w)?g()p?qqq,.2.5.2e w?vM(w)=supwM(w),K wg()?qqq,?OOO.nnn2.5.3e?qqq,?OOO,K w=g()g()?qqq,?OOO.1?!?9?O2.5?Oo!?q,?O2.5.1?X=(X1,X2,Xp)0 Np(,),Xi,Xj?Xij=ijiijj?q,?O?rij=aijaiiajj1?!?9?O2.5?Oo!?q,?O2.5.2?X=X(1)X(2)#Np(1)(2)#,11122122#!KX(1)X(2)?8X?B=12122?4?q,?O?B=12122=A12A1229X(2)?X(1)?112?4?q,?O?112=1n(A11 A12A122A21).