Multivariate statistics (2023)

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• Course requirements
• Topics of the final exam
• Lesson 1 (Linear algebra and random vectors, basics for the whole semester)
• Lesson 2 (Multivariate normal distribution)
• Lesson 3 (Parameter estimation in multivariate models)
• Addendum to Lesson 3: Cramer-Rao inequality for multidimensional parameter functions. Not an exam topic.
• Lesson 4 (ML estimation in multivariate normal models and the distribution of the estimators)
• Addendum to Lesson 4 (Multivariate normal distribution as an exponential family distribution)
• Supplementary material (slides to parameter space, ML estimation, Lukacs theorem, and derivation of the Wishart density). Only Lukacs theorem and ML estimation are included in the exam topics.
• Lesson 5 (Hypothesis testing on the multivariate normal mean vector)
• Lesson 6 (Multivariate regression)
• Addendum to Lesson 6 (Partitioned covariance matrices, partial correlations and Gaussian graphical models)
• Figure to the Addendum of Lesson 6
• Lesson 7 (Generalized linear models, ANOVA, time series, econometrics, examples). Time series and econometrics is not an exam topic.
• Lesson 8 (Principal Component and Factor Analysis)
• Lesson 9 (Canonical Correlation Analysis)
• Lesson 10 (Correspondence Analysis)
• Lesson 11 (Discriminant Analysis)
• Lesson 12 (Clustering and Multidimensional Scaling)
• Dynamic Factor Analysis. Not an exam topic.
• Table of notable distributions
• Notable distributions
• Percentile values of the standard normal, t, and chi-square distributions
• Percentile values of the F-distribution
• Formulas of statistical tests and regression
• ANOVA tables
• BMDP outputs
• Homework I. deadline: 30th October, 2023.
• Homework II. deadline: 4th December, 2023.
• The original paper of John Wishart
• A recent result (in English)
• A recent result (in French)
• Államvizsga tematika (MSC képzés)
• Closing (state) exam questions (MSC)