# 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

8518

6.0

##### Responsible teacher

Regina Maria Baltazar Bispo

Weekly - 4

Total - 56

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

Lectures by Zoom:

# Continuous evaluation:

`Exercise resolution - Exercises for the week (total of 12 exercise sheets, weighting 10%). `
`The grade in this component is proportional to the number of sheets delivered `
`(for example, a student who completed 10/12 sheets, has a grade in this component equal `
`to 17 values). All forms must be delivered via moodle, in pdf format, using the template `
`provided, in the respective week. `

`1st test - Test with consultation, taking the distance, `
`via moodle, with a weighting of 20%. The test will last 1h30m + 30m tolerance. `
`During the test, the teacher will be online, via Zoom (link to be made available in due `
`course) to clarify any doubts. The test is rated on a scale of 0 to 20. `

`2nd test - Test with consultation, to be performed at a distance, via moodle, with a `
`weighting of 20%. The test will last 1h30m + 30m tolerance. During the test, the `
`teacher will be online, via Zoom (link to be made available in due course) `
`to clarify any doubts. The test is rated on a scale of 0 to 20. `

`Work - Individual work of analysis of multivariate data. `
`The work will have a weight of 50% and will be delivered in the last class of `
`the semester. The work is classified on a scale of 0 to 20 values.`

# Appeal and note enhancement

`Remote written test (may be in person, if the number of students allows it), on a `
`single date, within the time specified in the academic calendar, with a weighting `
`of 100%. The exam will last 3 hours. The exam is rated on a scale of 0 to 20 points.`

## Subject matter

Presentation  of the Professor and the curricular unit

1. Revision of basic linear algebra concepts (Vectors and matrices. Basic operations .Transposition. Determinant of a matrix. Inverse of a matrix. Trace of a matrix. Eigenvalues ​​and eigenvectors.)

2. Multivariate Data

3. Multivariate Distributions

4. Inference on multivariate mean values

4.1 Inference over a mean vector

4.2 Comparison of two mean vectors

4.3 Comparison of more than 2 mean vectors

6. Analysis of covariance structure

6.1 Principal Component Analysis

6.2 Canonical Correlation Analysis

7. Classification and clustering analysis

7.1 Discriminant Analysis

7.2 Cluster Analysis

## Programs

Programs where the course is taught: