ABSTRACT

Significantly revised and expanded, Multivariate Statistical Analysis, Second Edition addresses several added topics related to the properties and characterization of symmetric distributions, elliptically symmetric multivariate distributions, singular symmetric distributions, estimation of covariance matrices, tests of mean against one-sided altern

chapter 1|11 pages

3. RANK AND TRACE OF A MATRIX

chapter |1 pages

(1.11)

chapter |29 pages

(1.12)

chapter |10 pages

(3.7)

chapter |2 pages

E(?(gT)-?(T))=0

chapter 3|2 pages

5. UNBIASEDNESS AND INVARIANCE

chapter 3|5 pages

7. MOST STRINGENT TESTS AND INVARIANCE

chapter |22 pages

(3.27)

chapter |1 pages

cov(Z, Z)=E(Z-E(Z))(Z E(Z))*. (4.10)

chapter |5 pages

(4.13)

chapter |19 pages

AND CHARACTERIZATIONS

chapter |27 pages

CORRELATION

chapter |10 pages

T=(T(N)), g(?)=(g(?))

chapter L|1 pages

'T=E(L'T**|T*)

chapter |1 pages

(5.24)

chapter X|1 pages

=(x,…, X), x=(x,…, x).

chapter |3 pages

(5.33)

chapter |2 pages

(5.45)

chapter |3 pages

(5.50)

chapter |1 pages

(5.62)

chapter 5|16 pages

3.4. Unbiased Estimation of Risk

chapter |3 pages

Plant XXXXXX

chapter |12 pages

(5.101)

chapter |1 pages

(6.1)

chapter |8 pages

(6.6)

chapter |4 pages

(6.25)

chapter |3 pages

S=CC, Y=C Xa, a=1,2,…, N-1,

chapter |9 pages

(6.40)

chapter |2 pages

(6.57)

chapter C|8 pages

=-A A'YY'(A+A'Y')

chapter |8 pages

(6.77)

chapter |5 pages

(6.91)

chapter |11 pages

([(sin O ) (sin O )

chapter |12 pages

REFERENCES

chapter 7|1 pages

2.1. Hotelling’s T-Test

chapter |1 pages

(7.14)

chapter |4 pages

(7.18)

chapter |1 pages

gSg'=I (7.28)

chapter |5 pages

gSg'=I=hTh'=?hTh'?'

chapter |7 pages

(7.39)

chapter |5 pages

(7.57)

chapter |3 pages

(7.71)

chapter |8 pages

(y-?Sl )'S (y-?Sl )=0.

chapter |2 pages

(7.81)

chapter |1 pages

(7.81a)

chapter |4 pages

(7.81c)

chapter |1 pages

(7.84)

chapter 7|1 pages

5.1. Test of Mean Vector

chapter |4 pages

(7.89)

chapter |14 pages

(7.94)

chapter |1 pages

(8.2)

chapter |4 pages

(8.7)

chapter |11 pages

(8.17)

chapter |1 pages

(8.43)

chapter |1 pages

(8.46)

chapter |1 pages

(8.49)

chapter |3 pages

(8.53)

chapter |1 pages

(8.63)

chapter 8|4 pages

3.1. The R-Test

chapter |8 pages

(8.74)

chapter |1 pages

(8.90)

chapter |2 pages

(8.94)

chapter |3 pages

(8.101)

chapter |1 pages

(8.105)

chapter |1 pages

(8.106)

chapter |3 pages

(8.110)

chapter |5 pages

(8.115b)

chapter |2 pages

(8.122)

chapter |5 pages

(8.127)

chapter |2 pages

(8.147)

chapter |1 pages

(8.156)

chapter |5 pages

(8.159)

chapter |1 pages

(8.170)

chapter |2 pages

(8.175) (ii)

chapter |1 pages

(8.179)

chapter |1 pages

(8.185)

chapter |10 pages

Location 123456789 10 11 12

chapter |2 pages

(8.205)

chapter |1 pages

(8.210)

chapter |1 pages

(8.215)

chapter |2 pages

(8.218)

chapter |2 pages

(8.224)

chapter 8|3 pages

8. COMPLEX ANALOG OF R-TEST

chapter 8|3 pages

9.1. The Sphericity Test (8.230)

chapter 8|2 pages

9.2. The Sphericity Test

chapter |5 pages

(8.241)

chapter |2 pages

(? , ? *, ?, ?*)

chapter |6 pages

(8.258)

chapter |3 pages

EXERCISES

chapter |17 pages

Replication 123456789 10

chapter |4 pages

(9.16)

chapter |5 pages

(9.32)

chapter |5 pages

(9.41)

chapter |18 pages

b=(tS+tS

chapter 9|4 pages

5. CONCLUDING REMARKS

chapter |11 pages

REFERENCES

chapter |2 pages

det(S-?I)=0. (10.5)

chapter |3 pages

(10.10)

chapter |4 pages

(B'SB-?I)ß=0.

chapter |5 pages

(10.27)

chapter |9 pages

(10.37)

chapter 11|5 pages

1. POPULATION CANONICAL CORRELATIONS

chapter |5 pages

(11.13)

chapter |4 pages

S-D=? ? '. (12.4)

chapter |2 pages

(12.10)

chapter |1 pages

(12.15)