Multivariate Statistical Analysis (DATA 130044)

Lecture Time and Venue:

Grading:

Reading Materials:

• Richard A. Johnson, Dean W. Wichern. "Applied Multivariate Statistical Analysis". Pearson; 6th Edition. [link]
• Theodore W. Anderson. "An Introduction to Multivariate Statistical Analysis". John Wiley & Sons Inc; 3rd Edition. [link]
• 张尧庭/方开泰. "多元统计分析引论". 科学出版社, 2015. [link]

Courseware (subject to changes):

• Sep 07: Introdution, Review of Linear Algebra and Optimization. [pdf]
• Sep 14: Random Vectors and Matrices, Random Samples, Generalized Variance. [pdf]
• Sep 21: Multivariate Normal Distribution, Linear Transformation, Marginal Distribution. [pdf]
• Sep 28: *Applications: Gaussian Smoothing, Zeroth-Order Optimization. [pdf]
• Oct 07: Singular Normal Distribution, Conditional Distribution, Characteristic Function. [pdf]
• Oct 12: Maximum Likelihood Estimator of Mean and Covariance, Distribution Theory. [pdf]
• Oct 19: Unbiasedness, Sufficiency, Completeness, Efficiency. [pdf]
• Oct 26: Asymptotic Normality, Bayesian Estimation, James–Stein Estimator. [pdf]
• Nov 02: Noncentral Chi-Squared Distribution, Hypothesis Testing for the Mean with Known Covariance. [pdf]
• Nov 09: Sample Correlation Coefficient, Tests for the Lack of Correlation. [pdf]
• Nov 16: The Likelihood Ratio Criterion, The Asymptotic Distribution of Sample Correlation, The Wishart Distribution. [pdf]
• Nov 23: The Density of Wishart Distribution, T²-Statistic and F-Distribution, The Inverted Wishart Distribution. [pdf]
• Nov 30: The Characteristic Function of Wishart Distribution, More Matirx Variate Distributions. [pdf]
• Dec 07: Revisiting Likelihood Ratio Criterion, Multivariate Analysis of Variance, Multivariate Linear Regression. [pdf]
• Dec 14: Bayesian Multivariate Linear Regression, (Kernel) Principal Component Analysis, Canonical Correlation Analysis. [pdf]
• Dec 21: Probabilistic Principal Component Analysis, The Expectation-Maximization Algorithm. [pdf]