17
Chapter 6. Comparison of Several Multivariate Means.
This chapter addresses comparison of several multivariate means. We begin with paired comparison
followed by repeated measurement. In these two settings, comparison of two multivariate means or
sever
47
Chapter 11. Discrimination and Classication.
Suppose we have a number of multivariate observations coming from two populations, just as in the
standard two-sample problem. Very often we wish to, by taking advantage of the characteristics of
the distrib
36
Chapter 9. Factor Analysis
Factor analysis may be viewed as a renement of the principal component analysis. The objective
is, like the P.C. analysis, to describe the relevant variables in study in terms of a few underlying
variables, called factors.
9.
41
Chapter 10. Canonical Analysis
Canonical analysis aims at nding the relation between two sets of variables, by singling out pairs
of random variables with highest hierarchical correlations. In every pair, one is a linear combination
of one set of varia
33
Chapter 8. Principal Components.
Principal component, abbreviated as P.C., analysis, was invented by Carl Pearson in 1901. The
aim is to create one or a few new variables by linearly combining the existing variables in study so
that the new variables,
26
Chapter 7. Multivariate Linear Regression Models.
Multivariate linear regression model is essentially several univariate linear regression models putting
together, with the errors being related with each. Here univariate (multivariate) means the respon
11
Chapter 5. Inferences About The Mean Vector
This chapter addresses the most basic and most standard statistical problem about the mean
of a population, given a standard one sample: some independent identically distributed (iid)
observations from the po
7
4.3. Likelihood and maximum likelihood estimation.
Suppose X1 , ., Xn are iid random p-vectors M N (, ). Their joint density is
n
f (x1 , ., xn )
1
=
(2 )p |
i=1
=
exp
1
2
1
expcfw_ (xi ) 1 (xi )
2
n
(xi ) 1 (xi )
i=1
n
np
log(2 ) log |
2
2
for xi Rp
Multivariate Statistical Analysis
Math4424
HKUST
Kani Chen (Instructor)
Chapter 1.
Introduction (Aspects of Multivariate Analysis.)
Multivariate analysis generally refers to a range of statistical techniques/methods which primarily
involves data with seve
4
Chapter 4.
The Multivariate Normal Distribution.
4.1. Some properties about univariate normal distributiona review.
Suppose X N (, 2 ), a univariate normal distribution with mean and variance 2 .
(i). Density:
(x)2
1
f (x) =
e 22 ,
x (, ).
2 2
The dens