多元统计分析第05章

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2、ýÿ¥§â±N¤««I§äeGݬ´!²~´¢1ÊÙ!O©ÛÃØ3=+,O©Û¯Kѱù£ã:kkmoNG1,G2,···,Gk,Ù©ÙA®(X®©Ù¼ê©OF1(x),F2(x),···,Fk(x),½5goNÔö).é

3、½#¬X,·ä§5g=oN.A~^O{k:ålO!BayesO!FisherO!ÅÚO!S0O.1ÊÙ!O©Û5.1ålO5.1ålOålOÄg:¬Ú=oNålC,Òä§áu=oN.ålO{¡*O{.1ÊÙ!O©Û5.1ålO!ê¼ål!!!êêê¼¼¼ååålll®küaG1ÚG2,'XG1´A)¬,G2B)Óa¬.A¬þp,Ù²þFݵ(1)=80,N°Ýσ12=0.25;éB,Ù²þFݵ(2)=75,°Ýσ22=4.8k

4、¬X0,ÿFݵ(0)=78,äT¬5g=oN?*þX0´A),e¡Ä«é5ål.PX0G1ÚG2é²åld21(x)Úd22(x),K2(x0−µ(1))2(78−80)2d1(x0)=2==16σ0.2512(x0−µ(2))2(78−75)2d2(x0)=2==2.25σ4.002dud22(x0)

5、^éål±éÑ©.:

6、(bµ(1)<µ(2)),-(x−µ(1))2(x−µ(2))2µ(1)σ2+µ(2)σ1def∗=→x==µσ2σ2σ1+σ212Uù«ålCOOK:(X∈G1,x>µ∗X∈G2,x≤µ∗1ÊÙ!O©Û5.1ålO!ê¼ålÑmoNê¼ål½Â½½½ÂÂÂ(5.1.1)oNGmoN,þþµ=(µ1,µ2,···,µm)0,ÝΣ=(σij)m×m,K¬XoNGê¼ål½Âd2(X,G)=(X−µ)0Σ−1(X−µ)1ÊÙ!O©Û5.1ålO!üoNålO!!!üüüoooNNN

7、ååålllOOO0.'''VVVgggküoNG1ÚG2,5gGiÔö(i)(i)(i)(i)0X(t)=(x(t1),(t2),···,(tm))i=(1,2);t=(1,2,···,ni),KþþµOþ1Xni1XniX¯(i)=(x(i),···,x(i))0=(¯x(i),x¯(i),···,X¯(i))0nt1ntm12miit=1t=1oNGΣiOSi(¡

8、

9、

10、SSS)1(i)Si=Ai=(slj)m×mni−11ÊÙ!O©Û5.1ålO!üoNålOXni(i

11、)(i)(i)(i)0Ù¥Ai=(X(t)−X¯)(X(t)−X¯)¡

12、Slt=1Xni(i)1(i)(i)(i)(i)s=(x−x¯)(x−x¯)ljn−1tltjit=1(l,j)=(1,···,m)1ÊÙ!O©Û5.1ålO!üoNålOb½Σ1=Σ2=Σ,ÝOXk1S=Ai=(slj)m×mn−ki=1¡SÜÜÜ¿¿¿Ù¥1X2Xni(i)(i)(i)(i)slj=(xtl−x¯)(xtj−x¯)n−ki=1t=1(l,j)=(1,···,m)1ÊÙ!O©Û5.1ålO!

13、üoNålO1.Σ1=Σ2OOO{{{O¬XüoNåld2(X,G1)Úd2(X,G2),OOK:(X∈G1,d2(X,G1)

14、^ê¼ål½Â9Ó{zê¼ålOúª:d2(X,G)=(X−X¯(i))0S−1(X−X¯(i))(1)i=X0S−1X−2[(S−1X¯(i))0X−1(X¯(i))0S−1X¯(i)(2)]2=X0S−1X−2Y(X)(3)i1ÊÙ!O©Û5.1ålO!üoNålO¤

15、±Oê¼ålUéX5¼êYi(X)O:Y(X)=(S−1X¯(i))0X−1(X¯(i))0S−1X¯(i)i2Yi(X)¡555OOO¼¼¼êêê,ai=S−1X¯(i)¡555XXXêêêþþþ,c=−1(X¯(i))0S−1X¯(i)¡~~~êêêi21ÊÙ!O©Û5.1ålO!üoNålO