ft f g
rp (|nTe
7
v j f u
dr5yvr r | ing pm d5y
r d
d f
0 u y7
f m f d f r d
l d r
p 0dE|0y5ihs 1 !u f B
T" T"
!i! zsd
5
5
" (
iy j E|Qp
d
l t d
d
iy j E
l d
q
=x
= (4, 6) . From the invariance principle of MLE, we know that the MLE of
1. MLE of :
1 P4
1/2 S V 1/2 , where S = (s )
)(xi x
!) =
can be calculated
n
n
ij 1i,j4 = 4
i=1 (xi x
! by: = V
0.5 0.25
1
3/6
, V = diag(s11 , . . . , s44 ). The calculatio
DEPARTMENT OF MATHEMATICAL AND COMPUTATIONAL SCIENCES
UNIVERSITY OF TORONTO MISSISSAUGA
STA437H5S LEC0101
Applied Multivariate Statistics
Course Outline - Winter 2017
Class Location & Time
Instructor
Office Location
Office Hours
Telephone
E-mail Address
C
STA437H1S/2005H1S
Applied Multivariate Analysis
Instructor: K. Knight (oce: Sidney Smith 5016G; e-mail: [email protected])
My oce is at the west end of the 5th oor.
Oce hours: Tuesdays from 10am to noon, or by appointment. Do not hesitate to contac
SOME PRACTICE PROBLEMS
1. (a) The R output below gives the results of a factor analysis of 5 variables using a single
factor. Note that R standardizes the variables to have mean 0 and variance 1.
Uniquenesses:
x1
x2
x3
x4
x5
0.605 0.383 0.389 0.084 0.089
STA 437/1005 Answers to Quiz #1 2010-09-27
1. Consider the following six observations of two variables:
100
95
110
100
100
95
20
18
22
20
21
19
a) [ 10 marks ] Find the sample mean vector for this data set.
Answer: [ 100, 20 ]0
b) [ 30 marks ] Find the sa
Practice Problems for Final Exam, STAT 437/2005
1. A normal random vector X has the property that, for an arbitrary vector c = (c1 , c2 , c3 ) , c X
follows a normal distribution with the mean c2 +c3 and the variance c21 +2c22 +3c23 3c2 c3 . Does
this inf
1. (Total 5 mk) A researcher considered three indices measuring the severity of heart attacks. The
values of these indices for n = 40 heart-attack
at a hospital emergency
room
patients arriving
46.1
101.3 63
71
= 57.3 and S = 63
produced the summary sta
STA 437/1005, Fall 2010 Assignment #1
Due at start of lecture on November 15. Please hand it in on 8 1/2 by 11 inch paper, stapled
in the upper-left corner, without any folder or other packaging around it. If really necessary,
you can submit it by email (
STA 437/1005, Fall 2009 Assignment #3
Due at the start of the lecture on November 30. (Note that due to lack of time, Ive
had to abandon the idea of an assignment with a two-part solution/critique form that I
discussed earlier.)
Please hand this assignmen
STA 437/1005, Fall 2009 Assignment #2
Due at the start of the lecture on November 2. Please hand it in on 8 1/2 by 11 inch paper,
stapled in the upper-left corner, without any folder or other packaging around it. Note
that Ive decided that only the last a
STA 437/1005, Fall 2009 Solutions to Assignment #1
Q1(a):
E(X1 ) = E(U1 ) + E(U2 ) + E( 1 ) = 0, and the same for X2 and X3 . The the mean vector is
= [0 0 0].
Since U1 , U2 , and 1 are independent, Var(X1 ) = Var(U1 )+Var(U2 )+Var( 1 ) = 1+1+22 = 6,
and
STA 437/1005, Fall 2010 Assignment #2
Due at start of lecture on December 6. Please hand it in on 8 1/2 by 11 inch paper,
stapled in the upper-left corner, without any folder or other packaging around it. If really
necessary, you can submit it by email (t
STA 437/1005, Fall 2009 Assignment #1
Due on October 8, during oce hours, or you can slip it under my door (SS6016A) if Im not
there. You might want to hand it in during the lecture on October 5, however. Please hand it
in on 8 1/2 by 11 inch paper, stapl