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Multivariate Statistics

Objectives

It is intended to familiarize the student with inference techniques for multivariate mean values ​​and covariance matrices, as well as multivariate linear models in Gaussian populations, dimensionality reduction methods, discrimination and data classification methods.

General characterization

Code

8518

Credits

6.0

Responsible teacher

Filipe José Gonçalves Pereira Marques

Hours

Weekly - 4

Total - 56

Teaching language

Português

Prerequisites

Basic concepts of analysis and intermediate level knowledge in Linear Algebra, Probabilities and Statistical Inference

Bibliography

Anderson, T. W. (2003), An Introduction to Multivariate Statistical Analysis, 3rd ed., J. Wiley & Sons, New York

Flury, B. (1997), A First Course in Multivariate Statistics, Springer. New York

Johnson, R. and Wichern, D. W. (2007), Applied Multivariate Statistical Analysis, 6th Edition, Prentice Hall, New Jersey

Morrison, D. F. (2004), Multivariate Statistical Methods, 4th Edition, Duxbury Press

Rencher, A. C. (1998), Multivariate Statistical Inference and Applications, John Wiley & Sons

Rencher, A. C. and Christensen, W. F. (2012). Methods of Multivariate Analysis, Third Edition, John Wiley & Sons

Zelterman, D. (2015). Applied Multivariate Statistics with R. Springer

Teaching method

Available soon

Evaluation method

1. Requirements

In order to be able to have admission the assessment of the subject, either by Continuous Assessment or by Exam, students must attend at least 2/3 of the classes.

2. Assessment

Continuous Assessment consists of the following assessment elements:

Test - weight: 60%

Practical work - weight: 40%

Any student with a final mark (weighted average) of 9.5 or higher will be approved. Students who have not passed the continuous assessment may take an Exam if they meet the UC requirements.

Students who pass the continuous assessment can improve their grade in the Exam.

Students with a final mark of 18 or more must take an oral exam to defend their mark. If they don''t take this exam, they will receive a mark of 18.

Subject matter

  1. Succint revisions (linear algebra, random variables and random vectors, confidence intervals and statistical inference)
  2. Introduction to Multivariate Statistics: the multivariate Normal distribution and the Wishart distribution
  3. Graphical representations and an outlier test 
  4. Inference for vectors of expected values
    1. Inference for a single vector of expected values
    2. Test of equality for two vectors of expected values
    3. Test of equality for several vectors of expected values
  5. Inference on covariance matrices
    1. Tests and Confidence Intervals for eigenvalues and the sphericity test
    2. The test of equality of several covariance matrices
  6. Analysis of covariance structures
    1. Principal Components Analysis (tests and confidence intervals for eigenvalues and the test for outliers revisited)
    2. Canonical Correlations Analysis and the Multivariate Linear Model (the test of independence of 2 sets of variables and tests for canonical correlations and for models and submodels)
  7. Classificatory Analysis and Clustering 
    1. Discriminant Analyis
    2. Cluster Analysis