Multivariate statistics (2023)

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: CramerRao 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 chisquare distributions

Percentile values of the Fdistribution

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)