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STA D37H (Winter 2012): Multivariate Analysis - Lecture Schedule

Tentative Lecture Schedule

  • Jan 9 -- 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.

  • Jan 16 -- 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.

  • Jan 23 -- Multivariate normal distributions (Chapter 4):
    MVN density function, properties of multivariate normal; Eigenvalues and eigenvectors; The sampling distribution of mean and covariance, Maximum likelihood estimation.
    Reading: Chapters 4.2 - 4.4

  • Jan 30 -- Inferences about the mean vector (Chapter 5)
    Finish MVN: Central Limit Theorem, Large-sample behavior of mean and covariance, Assessing the assumption of normality, QQ plots. 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.
    Reading: Chapters 4.5 - 4.6, Chapters 5.1 - 5.3

  • Feb 6 -- Inferences about the mean vector (Chapter 5) and Comparisons of Several Multivariate Means (Chapter 6)
    Confidence Regions, Simultaneous Confidence Statements, The Bonferroni Method, Large Sample Inferences, Paired Comparisons, and Comparing Mean Vectors from Two Populations.
    Reading: Chapters 5.4 - 5.5 Chapters 6.1 - 6.3

  • Feb 13 -- Comparisons of Several Multivariate Means (Chapter 6)
    Comparing Mean Vectors from Two Populations, Univariate ANOVA, One-Way MANOVA, Review for the Midterm.
    Reading: Chapters 6.1 - 6.4

    Midterm is on Friday 27, 2012:
    You can use a nonprogrammable calculator and an 8 by 11 inch Crib Sheet - Single-sided.

  • Mar 5 -- Principal Component Analysis (Chapter 8)
    Population Principal Components, Summarizing Sample Variation by PCs, Large Sample Inference, Testing for the Equal Correlation Structure.
    Reading: Chapters 8.1 - 8.5

  • Mar 12 -- Factor Analysis (Chapter 9)
    Orthogonal Factor Model, Covariance Structur of the 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.
    Reading: Chapters 9.1 - 9.6

  • Mar 19 -- Discrimination and Classification (Chapter 11)
    Classification for two populations, Expected Cost of Misclassification, Total Probability of Misclassification,Classification with Two Multivariate Normal Populations, Fisher's Discriminant Analysis, Evaluating Classification Functions.
    Reading: Chapters 11.1 - 11.4

  • Mar 26 -- Canonical Correlation Analysis (Chapter 10)
    Canonical Variates, Canonical Correlations, Interpreting Canonical Variables, The Sample Canonical Variates, Large Sample Inference.
    Reading: Chapters 10.1 - 10.4, 10.6.

  • April 2 -- Multivariate Linear Regression (Chapter 7)
    Linear Regression, Least Squares Estimation, Multivariate Multiple Regression. Review for the Final Exam.
    Reading: Chapters 7.1 - 7.3, 7.7


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