Topic Two:
Matrix Algebra and Random Vectors
1
Preview
Motivation:
A multivariate measurement will be represented as
a vector.
A sample of multivariate measurements will be
represented as a matrix.
Goals:
Review some important topics from linear al
STAT 636: Applied Multivariate Analysis
Fall 2016
Instructor: Dr. Alan Dabney
Office: 459B Blocker Building
Email: adabney@stat.tamu.edu
Office Hours: By appointment.
Course Description: This course introduces foundations of multivariate analysis includin
STAT 636, Fall 2016 - Assignment 4
Due Monday, Nov. 21, 11:55pm central
Online Students: Submit your assignment through WebAssign.
On-Campus Students: Email your assignment to the TA.
1. Consider the matrix of distances for four items
0
3 0
2 4 0
5 1 7
STAT 636, Fall 2016 - Assignment 3
Due Sunday, Oct. 30, 11:59pm Central
Online Students: Submit your assignment through WebAssign.
On-Campus Students: Email your assignment to the TA.
1. Consider the hof data. In this problem, you will use both LDA and QD
STAT 636, Fall 2016 - Assignment 1
Solutions
1. The Oxygen data contain p = 4 oxygen volume measurements for 25 males and 25 females. The
variables are X1 : oxygen volume (L/min.) while resting, X2 : oxygen volume (mL/kg/min.)
while resting, X3 : oxygen v
STAT 636, Fall 2016 - Assignment 2
Solutions
1. Find the maximum likelihood estimates of the 2 1 mean vector and the 2 2 covariance
matrix based on the random sample
3 6
4 4
X=
5 7
4 7
, the vector of sample means, and the MLE of is what
The MLE of i
STAT 636, Fall 2016 - Assignment 1
Due Sunday, September 11, 11:55pm Central
Online Students: Submit your assignment through WebAssign.
On-Campus Students: Email your assignment to the TA.
1. The Oxygen data contain p = 4 oxygen volume measurements for 25
STAT 636, Fall 2016 - Assignment 2
Due Sunday, October 9, 11:55pm Central
Online Students: Submit your assignment through WebAssign.
On-Campus Students: Email your assignment to the TA.
1. Find the maximum likelihood estimates of the 2 1 mean vector and t
Similarity Measures
Most efforts to produce a rather simple group structure from a complex data set require
a measure of closeness, or similarity. There is often a great deal of subjectivity
involved in the choice of a similarity measure. Important consid
Topic Three:
Sample Geometry and Random
Sampling
1
Preview
Motivation:
Geometrical representation makes the data easier
to visualize and understand.
While there are many ways to obtain data, random
sampling affords many advantages.
Goals:
Demonstra
Topic Six: Inferences About
Multiple Mean Vectors
1
Preview
Motivation:
The one-sample inferential techniques we just
learned can be easily extended to the two-sample
setting.
For comparing 3 or more means, we can similarly
generalize ANOVA to the mu
Topic Four:
The Multivariate Normal
Distribution
1
Preview
Motivation:
The univariate normal distribution plays a very important
role in univariate statistics, both as an assumed population
model and in enabling inference with large sample sizes.
Sim
Population Principal Components
Algebraically, principal components are particular linear combinations of the p random variables X1 , X2 , . . . , Xp . Geometrically, these linear combinations represent the selection of a new coordinate system obtained by
Topic Five: Inferences About a
Mean Vector
1
Preview
Motivation:
Statistical inference is the process of drawing
confident conclusions about a population based on a
sample. Example applications are confidence intervals
and hypothesis tests.
Because p
Multivariate Statistics
Dr. Alan Dabney
Associate Professor
Department of Statistics
Texas A&M University
1
Topic One:
Introductory Material
2
What does multivariate mean?
Univariate: Record single variable for each individual.
Examples:
Survival time