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STA D37H (Winter 2013): Multivariate Analysis - Lecture Schedule

Tentative Lecture Schedule

  • Lecture 1 -- Organization of Data (Chapter 1), Marix Algebra (Chapter 2):
    Topics and applications of multivariate analysis, Data organization, Sample statistics, Basics of Vector and Matrix Algebra, Positive Definite Matrices, Spectral Decomposition.
    Reading: Chapters 1.1 - 1.6, Chapters 2.1 - 2.3.

  • Lecture 2 -- Random Vectors (Chapter 2), Random Sampling (Chapter 3):
    Random vectors and matrices; Matrix Inequalities and Maximization; Random Samples; Sample Means, Covariances, Correlations for random vectors; Linear Combinations of Variables; Estimation of mean, covariance from sample statistics; Start of discussion of normal distribution.
    Reading: Chapters 2.5 - 2.7, Chapters 3.1 - 3.3, 3.5 - 3.6, Chapters 4.1 - 4.2.

  • Lecture 3 -- Multivariate normal distributions (Chapter 4):
    MVN density function, properties of multivariate normal; Eigenvalues and eige nvectors; The sampling distribution of mean and covariance, Maximum likelihood estimation. Central Limit Theorem, Large-sample behavior of mean and covariance, Assessing the assumption of normality, QQ plots.
    Reading: Chapters 4.2 - 4.6

  • Lecture 4 -- Inferences about the mean vector (Chapter 5)
    Start discussion of testing hypotheses about mean of univariate with t-statistic and multivariate normal distribution with Hotelling's T2 statistic, T2 and likelihood ratio tests. Confidence Regions, Simultaneous Confidence Statements, The Bonferroni Method, Large Sample Inferences.
    Reading: Chapters 5.1 - 5.5

  • Lecture 5 -- Comparisons of Several Multivariate Means (Chapter 6)
    Paired Comparisons, and Comparing Mean Vectors from Two Populations. Comparing Mean Vectors from Two Populations. Review for Midterm.
    Reading: Chapters 6.1 - 6.4

    Midterm is on Monday 25, 2013:
    You can use a nonprogrammable calculator and an 8 by 11 inch Crib Sheet - Single-sided .

  • Lecture 6 -- Principal Component Analysis, start with Factor Analysis (Chapters 8,9)
    Population Principal Components, Summarizing Sample Variation by PCs, Large Sample Inference, Orthogonal Factor Model, Covariance Structur of the Factor Model.
    Reading: Chapters 8.1 - 8.5, 9.1 - 9.2

  • Lecture 7 -- Factor Analysis, Discrimination and Classification (Chapter 9,11)
    Orthogonal Factor Model, Methods of Estimation, The principal components method, The maximum likelihood method, A large sample test for the number of common factors, Factor rotation. Classification for two populations.
    Reading: Chapters 9.2 - 9.6, 11.1 -11.2.

  • Lecature 8 -- Discrimination and Classification, Canonical Correlation Analysis
    Total Probability of Misclassification,Classification with Two Multivariate Normal Populations, Fisher's Discriminant Analysis, Evaluating Classification Functions. Canonical Variates, Canonical Correlations, Interpreting Canonical Variables,
    Reading: Chapters 11.2 - 11.4, Chapters 10.1 - 10.2

  • Lecature 10 Canonical Correlation Analysis
    Canonical Variates, Canonical Correlations, Interpreting Canonical Variables, The Sample Canonical Variates, Large Sample Inference. Review for the Final Exam.
    Reading: Chapters 11.2 - 11.4, Chapters 10.1 - 10.4, 10.6.

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