多元统计分析第07章.pdf-得力文库

资源描述

《多元统计分析第07章.pdf》由会员分享，可在线阅读，更多相关《多元统计分析第07章.pdf（50页珍藏版）》请在得力文库 - 分享文档赚钱的网站上搜索。

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?

3、xl?x2(?,n?:?X?G.1?!?7.1 oN?!?d?w?n?:?Xx1?x2?k?l?5,?l?O*?C?x1?x2?/L.w,XJ?x1?x2?,o?3?L&E?k?.?=C?:(Z1=cos()X1+sin()X2Z2=sin()X1+cos()X2L?=C?&E8?Z1?&E?1?!?7.1 oN?!?!?X=(X1,X2,Xp)0p?,?E(X)=,?D(X)=0.1?Z1=a0X?3?a01a1=1e,Var(Z1)?.?4?flK,.?KFf,(a1)=Var(a1X)(a01a1 1)=a01a1(a01a1 1),?(a1=2(I)a1=0=a01a1 1=0?w?,

4、?A?,a1?A?A?,?|?=z?A?A?flK.1?!?7.1 oN?!?nnn7.1.1?X=(X1,X2,Xp)0p?,D(X)=0.0?A?1 2 p 0,a1,a2,ap?A?A?.KX?1i?Zi=a0iX.?Z=(Z1,Z2,Zp)0p?,K?Zi(i=1,p)?gX?1i?:1Z=A0X,A?2D(Z)=diag(1,p),=?C?Z?31 2 p1?!?7.1 oN?n!?5?nnn!?555?P=(ij),=diag(1,p),?1 2 p?A?,a1,a2,ap?A?A?.oN?kXe5?:555?1D(Z)=,=p?:Var(Zi)=i(i=1,p),?p?.555?

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

9、j?S?OR?oN?O,?U?!?=?.1?!?7.2?!?9?5?!?999?555?b*?fiIOz,?R.R=1n 1X0XP?R?p?Z1,Z2,Zp,1 2 p 0?R?A?,a1,a2,ap?A?A?,PA=(a1,a2,ap)?.1?!?7.2?!?9?5?w,1i?Zi=a0iX.?1t?X(t)=(xt1,xtp)?Zi?L?“,?1t?3i?,P?zti.?:z11z12z1pz21z22z2p.zn1zn2znp=Z0(1)Z0(2).Z0(n)def=(Z1,Z2,Zp)1?!?7.2?!?9?5?5?:555?1Z=1nnXt=1Z(t)=0Z0iZj=(0(n 1)

10、i?i 6=j?,1i?1j?.555?2Ppi=1i=p.kp?Zk?zzz;qPmi=1i/p?Z1,Zm?OOO?zzz.555?3?k?5.1?!?7.2?!?9)”?8?z?(?,?U?Z1,Zm(m P0,?cm?,k?*?m?:zij=a0jX(i)=a1jXi1+a2jXi2+apjXip(i=1,nj=1,m)1?!?7.3?APZj=(z1j,z2j,znj)0?1j?ng?(j=1,2,m).|?5?3,?d?OC?Xk?.PXk=(x1k,x2k,xnk)0?xik=ak1zi1+akmzimX=x11x1p.xn1xnpdef=(X1,Xp)1?!?7.3?A?y:p

12、m)Zm|2=1(ai1 aj1)2+m(aim ajm)21?!?7.3?A?!?Ia(C?a)?(Zk,Xi)=pkaikdef=ik?2(1 rij)=(i1 j1)2+(im jm)2erij 1,Kk(i1 j1)2+(im jm)2 0=|Xi Xj|0,=r1i?C?1j?C?A8?a.1?!?7.3?A?!?Ia(C?a)7.3.1?CCC.aaaflflflKKK128?cIf?1?,z?16?I:?p(X1),?p(X1),9?(X1),?p(X1),?(X1),e?(X1),?(X1),+?(X1),c9(X1),?(X1),p?(X1),p?(X1),E?(X1),?(

13、X1),?(X1),?(X1).16?R?S(?,?n?).l?R?u?1?,16?I?1a.1?!?7.3?A?!?Ia(C?a)1?!?7.3?A?!?Ia(C?a)1?!?7.3?A?!?Ia(C?a)1?!?7.3?A?!?Ia(C?a)1?!?7.3?A?!?a?!?aaap?C?*?ng,?n?,PX(i)=(xi1,xip)?1i?,U?l?C?a,=e|X(i)X(j)|0r1i?1j?8?a.?X X,?|X(i)X(j)|X(i)X(j)|?X(i)=xi1.xip=a11a1m.ap1apm=zi1.zim1?!?7.3?A?!?a=(a1,am)zi1.zim|X(i)

14、X(j)|2=|a1(zi1 zj1+am(zim zjm)|2=(zi1 zj1)2+(zim zjm)2?r?p?m:?C?=z?m(m p)?m:?C?.e?m=2,n?:?3?L?,|:?5?a.1?!?7.3?A?!?a7.3.2?C.aflKY7.3.1E,|12816?I?*?128?C”?1a=?aflK?r128?Aaza?;.?LT?L?C”?a?”?):?m=2,?O?Z(i)=(zi1,zi2)0(i=1,2,128).r128?:?L3?|?r128?:?a?1?!?7.3?A?!?a1?a?k25?:?8%Z(25);1?a?k14?:?8%Z(114);1na?k

15、9?:?8%Z(89);1oa?k7?:?8%Z(112);1a?k12?:?8%Z(9);18a?k20?:?8%Z(47);1?a?k8?:?8%Z(118);?.?C?)?U25:14:9:7:12:20:8?5)?5?avkr128?:?)3S?k33?U8?a?AN/?1?!?7.3?An!?SX?nnn!?SSSXXX?p?oNX?1?“8?,?SflK?3S?IX?SflKX,a?L?1?K?L?IkX?!?*/?IflKn?/“?S?IX?J?1?Z1IOz?X=(X1,X2,Xp)0?1?d?5?Z1?IOzC?X1,X2,Xp?n?r.XJ?n?C?5?L?5k?C?Z?J

16、?Z11?!?7.3?An!?SX?,?du1?Z1Au?C?Z1?&E?!?p?n?C?d?u?EX?S?1?!?7.3?An!?SX?AAA:?(1)1?Z1?oU?5?S?XJZ1=a11X1+a21X2+a31X3+ap1Xp?Xai1(i=1,p)Qk?qkK?Cq?Z1?C?X1,X2,Xpk?,?K?Z1k?US?,?UZ1?S?.(2)?eZ2,Z3,Zp?5?E?S?Zk(k=2,p)?C?X1,X2,Xpk?,?K?(3)D?;?1?(?rD?;N?&E5?1?1?!?7.3?Ao!?8ooo!?8883?C?Y?p?gC?X1,Xp?8?.?gC?mk?r?5?5?|;?

17、8?8X?O?J?|?5?dcm?5?8?.?Y=b0+b1Z1+bmZm(m p)?Qz?8?(?C?m?5?5?K?,?8?8?.?)”?5?E,5?C?5|?*?C?k?(3?8?q_C?C?C?8?1?!?7.3?Ao!?8?C?mk?r?5?qkA?8?J?7.3.3L?8?o?Y?n?gC?ISo?x1?x2o?x3?10J?m?Xy8?1949?1959c?11c?L7.6?8?o?o?!?o?X“1?!?7.3?Ao!?81?!?7.3?Ao!?81?!?7.3?Ao!?81?!?7.3?A!?u?!?uuu?D(X)=,XJ?=p?m?rp?5u?flK?=z?p?5u?flK?=?m?|?X?p?Z1,Z2,Zp(?)d?O?p?p?n?C?rp?5u?flKz?p?n?C?5u?5u?u?Su?|?5?Icm(m p)?5u?

展开阅读全文