# 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

Regina Maria Baltazar Bispo

##### 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

`Lectures will be presential (if possible, to be confirmed). `

`It is intended that the classes work according to an essentially interactive teaching model, `

using practical exercise resolution and data analysis in R environment.

### Evaluation method

**Continuous evaluation:**

It includes the following components:

*1st mini-test*(MT1)- Test with consultation, to be carried out in a computer lab, in person, through moodle, with a weight of 25%. The test will last for 2 hours. The test is rated on a scale of 0 to 20 points (no minimum rating).*2nd mini-test*(MT2)- Test with consultation, to be carried out in a computer lab, in person, through moodle, with a weight of 25%. The test will last for 2 hours. The test is rated on a scale of 0 to 20 points (no minimum rating).*Work*(T)- Individual work of multivariate data analysis. The work will have a weight of 50%. The work is rated on a scale of 0 to 20 values.

Final grade calculation formula (NF): NF = 0.25 x (MT1+ MT2) + 0.5 x T (partial grades rounded to 1 decimal place)

**Resource (Improvement)/Special**: In-person written test to be held on a single date, within the period provided for in the academic calendar, with a weight of 100%. The exam will last for 3 hours. The exam is rated on a scale from 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

5. Inference about covariance matrices

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: