1. Introduction to multivariate data
1.1 Books
Chateld, C. and A.J.Collins, Introduction to multivariate analysis. Chapman & Hall
Krzanowski, W.J. Principles of multivariate analysis. Oxford.2000
John
3. Multivariate Normal Distribution
The MVN distribution is a generalization of the univariate normal distribution which has the
density function (p.d.f.)
1
f (x) = p
2
where
2
= mean of distribution,
4. Hypothesis testing (Hotellings T2 -statistic)
Consider the test of hypothesis
H0 :
HA
=
=
0
1
6=
0
4.1 The Union-Intersection Principle
W accept the hypothesis H0 as valid if and only if
H0 (a) : a
5. Discriminant Analysis (Classication)
Given k populations (groups)
for a set of p measurement x.
1 ; :;
k;
we suppose that an individual from
j
has p.d.f. fj (x)
The purpose of discriminant analysis
MT3732: Multivariate Statistics
Class exercise 2
Invariance of Hotellings T2 test
for linear contrasts
The weight of cork deposited in the four directions N; E; S; W was measured for 28 trees.
The sam