Stat 543: Applied
Multivariate Statistical Analysis
Spring
2012
Week
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Date
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Topics
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Sections in
the Book
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Homework
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Homework Due
Date
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Announcements
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1 |
01/23/12 |
Syllabus, Tentative
Schedule, Application of Multivariate Methods, |
1.1, 1.2 |
2.1, 2.2 , 2.3, 2.4*, 2.5, 2.6* |
01/30/12 |
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01/24/12 |
Data Organization, |
1.3 |
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01/25/12 |
R-Script for describing data,
Basics of Matrix Algebra |
1.3, 1.4, 2.1, 2.2 |
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01/27/12 |
Basics of Matrix Algebra, |
2.2 |
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2 |
01/30/12 |
Positive Definite Matrices,
Spectral Decomposition, Square Root and Power Matrices |
2.3, 2.4 |
2.11 (do not use the hint), 2.21, 2.25, 2.27, the two problems
assigned in class* |
02/10/12 |
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01/31/12 |
Examples, Random vector and
Matrices, mean vector, covariance and correlation matrices, |
2.5, 2.6 |
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02/01/12 |
Covariance and correlation
matrices, Linear Combinations, Random Sampling |
2.6, 3.1, 3.3 |
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02/03/12 |
Generalized Variance,
Multivariate Statistics as Matrix Operations, Singularity of S, |
3.4, 3.2, 3.5 |
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3 |
02/06/12 |
Statistics for Linear
Combinations, The Geometry of the Sample, |
3.6, |
3.2, 3.7,3.15, 3.18, the two starred problems assigned
in class |
2/17/12 |
(1) A2=A implies rank(A)=tr(A). (2) |
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02/07/12 |
The Multivariate Normal
Distribution: Pdf, mgf,
Linear Combinations, Marginal |
4.2 |
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02/08/12 |
The Multivariate Normal
Distribution: Independence, Conditionals; Statistical Distance; Maximum
Likelihood Estimation |
4.2, 4.3 |
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02/10/12 |
Sampling Distributions of
Basic Multivariate Statistics, Large Sample Properties, Assessing Multivariate
Normality |
4.4, 4.5, 4.6 |
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4 |
02/13/12 |
Using R for Assign Normality,
Chi-Squared Plot, Tests for Multivariate Normality |
4.6 |
4.29, 4.36,
4.37, 4.39 |
2/27/12 |
(1) Likelihood function for Power transformation (2) One of the problems from the results for the
Multivariate Normal Distribution |
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02/14/12 |
Mardia’s (1972, 1974), Royston’s (1983), Henze
and Zirkler’s (1990), Szekeley and Rizzo
(2006) Tests for Multivariate Normality, Detecting Outliers, Box-Cox
Transformation |
4.7, 4.8 |
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·
C. J. Mecklin and D. J. Mundfrom
(2005). A Monte Carlo Comparison of the Type I and Type II Error Rates of
Tests of Multivariate Normality, Journal of Statistical Computation and
Simulation, 75, 93-107. |
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02/15/12 |
Test for the Mean Vector,
Confidence Regions |
5.1, 5.2, 5.3, 5.4 |
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02/17/12 |
Confidence Regions, Simultaneous Confidence Intervals |
5.4 |
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5 |
02/20/12 |
President’s Day---No Class. |
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02/21/12 |
Large Sample Inference, Missing Data Mechanisms |
5.5, 5.7 |
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02/22/12 |
Inference about the Mean
Vector in the Presence of Missing Data |
5.7 |
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02/24/12 |
Missing Data, The Assumption
of Independence, Multivariate Paired-Sample Test, Repeated Measures Analysis |
5.7, 5.8, 6.1, 6.2 |
5.9, 5.15*, 5.16*,
5.18, 5.20, 5.23 |
03/02/12 |
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6 |
02/27/12 |
Repeated Measures Analysis,
R-Example |
6.2 |
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02/28/12 |
R-Example, Inference with Two
Independent Samples |
6.2, 6.3 |
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02/29/12 |
Inference with Two Independent
Samples |
6.3 |
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03/02/12 |
Behrens-Fisher Problem, Large
Sample Inference |
6.3 |
·
6.16, 6.19, 6.20,
6.21. For Statistics Students (1) Derive LRT for testing H_0: C mu=0. (2) T^2
is invariant to the choice of contrast matrix. |
03/09/12 |
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7 |
03/05/12 |
One-Way MANOVA, |
6.4 |
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03/06/12 |
One-Way MANOVA, Simultaneous
Inference |
6.4, 6.5 |
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03/07/12 |
Simultaneous Inference, Box’s
M-Test for equality of Covariance Matrices |
6.5, 6.6 |
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03/09/12 |
Two-way MANOVA |
6.7 |
6.25, 6.27, 6.31, 6.33 |
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For Statistics
Students: (1) Derive LRT for testing H0:mu_1-mu_2=delta_0 when samples come
from two normal populations with equal covariance matrix (2) Show that Wilks’
Lambda Statistis for one way MANOVA depends on the
data only through the eigenvalues of BW^{-1}. |
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8 |
03/12/12 |
Two-way MANOVA, Profile
Analysis |
6.7, 6.8 |
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·
Srivastava, M.S. (1987). Profile Analysis of Several groups.
Comm. in Stat. Theory & Methods. 16, 909-926. |
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03/13/12 |
Profile Analysis |
6.8 |
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03/14/12 |
Profile Analysis, Growth Curve
Analysis |
6.9 |
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03/16/12 |
Growth Curve Analysis |
6.9 |
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9 |
03/19/12 |
Multivaraite Multiple Regression |
7.7 |
6.39, Handout, 7.25, 7.26 |
03/27/12 |
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03/20/12 |
Multivariate Multiple
Regression |
7.8 |
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03/21/12 |
Multivariate Multiple
Regression |
7.9 |
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03/23/12 |
Population Principal
Components Analysis |
8.1, 8.2 |
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10 |
03/26/12 |
Population PCA, PCA under Normality, Standardizing the
Variables |
8.2 |
8.13 (a), (b)
and (c), 8.22, 8.26, 8.27 |
04/10/12 |
For Statistics Students: (1) Find the eigenvalues for the equi-correlation
covariance structure. (2) Do problem 8.9. |
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03/27/12 |
PCA for Covariance with
Special Structure, Sample PCA |
8.2 |
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03/28/12 |
Sample PCA, Examples--Turtle
Data, WAIS Data, 1984 Olympic Women’s
Athletics data |
8.3 |
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03/30/12 |
Graphing the PCs, Large Sample
Inference |
8.4, 8.5 |
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11 |
04/09/12 |
Large Sample Inference,
Canonical Variates and Canonical Correlations |
8.5, 10.1 |
10.7*, 10.9, 10.12, 10.16, 10.18, One starred problem
was assigned in class |
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04/10/12 |
Standardization, Interpreting
the Canonical Variates, Sample Canonical Variates and Correlations, Examples |
10.2 |
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04/11/12 |
Examples, Matrices of Errors
of Approximation |
10.2, 10.3 |
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04/13/12 |
Proportion of Explained Sample
Variance, Large Sample Inference |
10.3, 10.4, 10.5 |
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12 |
04/16/12 |
Separation and Classification
for Two Populations, Minimum ECM and TPM classifiers |
11.1, 11.2 |
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04/17/12 |
Classification for Two
Multivariate Normal Populations with Equal and Unequal Covariances,
Fishers Approach |
11.3 |
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04/18/12 |
Fishers Approach , Evaluating
Classification Functions |
11.3, 11.4 |
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04/20/12 |
Evaluating Classification
Functions, Example |
11.4 |
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13 |
04/23/12 |
Classification with Several
Populations |
11.5 |
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04/24/12 |
Classifications with Several
Populations, Example |
11.5 |
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04/25/12 |
Example Continued, Fisher’s
Approach |
11.5, 11.6 |
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04/27/12 |
Fisher’s Approach, Example,
Dimensionality, Large Sample Inference |
11.6, 8.6 from Rencher(2002) |
11.7*, 11.24, 11.30, 11.33, 11.35 |
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·
Section 8.6 from
A. C. Rencher, Methods of Multivariate Analysis,
Wiley 2002. |
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14 |
04/30/12 |
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05/01/12 |
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05/02/12 |
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05/04/12 |
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15 |
05/11/12 |
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