多元统计分析第07章.pdf
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1、1?!?1?!?June 15,20081?!?7.1 oN?7.1 oN?3?&E?KeC?L?1?Zn?z?p?C?m?1?n1?!?7.1 oN?!?!?X=(X1,X2,Xp)0p?,?E(X)=,?D(X)=.?5C?:Z1=a01X=a11X1+a21X2+ap1Xp,Z2=a02X=a12X1+a22X2+ap2Xp,Zp=a0pX=a1pX1+a2pX2+appXp,?Var(Zi)=a0iai(i=1,2,p)Cov(Zi,Zj)=a0iaj(i,j=1,2,p)1?!?7.1 oN?!?p?LC?”&E”.eFZ15?U?N?5?p?C?X=(X1,Xp)0,7La1?,K
2、?“u?.?a01a1=1.3?v?a1,Var(Z1)?,Z1?1?.XJ1?v?L?C?&E,?Z2,?FZ2?E?Z1?&E.Cov(Z1,Z2)=a02a1=0.Z2,?3a02a2=1?Cov(Z1,Z2)=a02a1=0e,a2Var(Z2)?.1?!?7.1 oN?!?7.1.1?X=(X1,X2,Xp)0p?,Zi=a0iX?X?1?,XJ:1a0iai=1(i=1,p)2?i 1?,a0iaj=0(j=1,i 1)3Var(Zi)=max0=1,0aj=0(j=1,i1)=Var(0X)1?!?7.1 oN?!?B,?3?m?A?.?kn?z?k?*?C?xl?x2,3dC?
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5、2Ppi=1ii=Ppi=1i,Ppi=1ii?oooNNNX?ooo?(ooo.?)d5?oNX?o?)?,?3m(m p),Pmi=1iiPpi=1i,=p?C?J?o&E?Icm?5?O.1?!?7.1 oN?n!?5?555?3?Zk?C?Xi?X(Zk,Xi)?(Zk,Xi)=pkaik/iir?Zk?C?Xi?X?fffKKK?555?4Ppk=12(Zk,Xi)=Ppk=1ka2ikii=1(i=1,2,p)555?5Ppi=1ii2(Zk,Xi)=k(k=1,p)1?!?7.1 oN?n!?5?7.1.2?k/Ppi=1i?Zk?zzz,Pmi=1i/Ppi=1i?Z1,Zm?
6、OOO?zzz.7.1.3?cm?Z1,Zm?C?Xi?z(m)i?Xi?Z1,Zm?X?,?u(m)i=mXk=1ka2ik/ii.1?!?7.1 oN?n!?5?7.1.1?X=(X1,X2,X3)0?=120250002X?9?C?Xi?zi(i=1,2,3)?A?1=3+8,2=2,3=3 8,?A?a1=(0.383,0.924,0.000)0a2=(0,0,1)0a3=(0.924,0.383,0.000)01?!?7.1 oN?n!?5?Z1=0.383X1 0.924X2Z2=X3Z3=0.924X1+0.383X2?m=1?,Z1X?z?(3+8)/8=72.8%?m=2?,
7、Z1?Z2X?z?97.85%.1?!?7.1 oN?n!?5?m?Xi?z(m)i.i(Z1,Xi)(Z2,Xi)(1)i(2)i10.92500.8560.8562-0.99800.9960.99630.00010.0001.000d?,?m=1?,Z1?zfi?72.8%,?n?,?Z1X3?z?0,?Z1vk?X3?&E,?,?Z1,Z2Xi?z?p.1?!?7.1 oN?o!IOzC?95?ooo!IIIOOOzzzCCC?999555?Xi=Xi E(Xi)VarXi=Xi ii(i=1,2,p)?IOz?C?.555?1D(Z)=diag(1,p),?1 2 p?R?A?.555
8、?2Ppi=1i=p1?!?7.1 oN?o!IOzC?95?555?3?Zk?IOzC?Xi?X?(Zk,Xi)=qkaik?ak=(a1k,apk)0RA?k?A?.555?4Ppk=12(Zk,Xi)=Ppk=1k(aik)2=1(i=1,2,p)555?5Ppi=12(Zk,Xi)=k(k=1,p)1?!?7.2?7.2?3SflK,?,I?L?5?O.?:x11x12x1px21x22x2p.xn1xn2xnp=X0(1)X0(2).X0(n)1?!?7.2?X?:S=1n 1nXt=1(X(t)X)(X(t)X)0def=(sij)ppR=(rij)pp,?rij=sijsiisj
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