# 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

Classes are based on theoretical exposition and examples analysis, using practical exercises and data analysis in R

### Evaluation method

# Continuous evaluation:

Continuous evaluation will be done through 3 evaluation elements:

- 1st assessment - Test to be carried out in class with a weight of 40%. The test will last 2 hours. The test is rated on a scale of 0 to 20 values.

- 2nd assessment - Test to be performed in the classroom with a weighting of 40%. The test will last 2 hours. The test is rated on a scale of 0 to 20 values.

- 3rd evaluation - Individual work to be done with the support of the R software (the use of RMarkdown is valued). The work will have a weight of 20% and will be delivered in the last class of the semester. The work is rated on a scale of 0 to 20 values.

The student obtain approval (continuous assessment) if the weighted average of the three assessment elements is greater than or equal to 9.5 values.

If a student does not attend one of the assessments, this assessment element will be rated 0.0 for the final grade.

# Appeal and note enhancement

In this assessment (appeal or improvement) the student can choose between the following modes of assessment:

1. Exam + Work:

- Examination to be carried out on a single date, within the period of appeal provided for in the academic calendar, with a weight of 80%. The exam will last 3 hours. The exam is rated on a scale of 0 to 20 values.

- Individual work to be done with the support of R software (the use of RMarkdown is valued). The work will have a weight of 20 \% and will be rated on a scale of 0 to 20 values.

2. Examination to be performed on a single date, within the period of appeal provided for 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 values.

The student obtain approval in the course at the time of appeal if the weighted average of the two assessment elements (exam - 80 \%, and work - 20 \%) is greater than or equal to 9.5 values or if the exam grade is greater than or equal to to 9.5 points (in case of opting for exam with 100% score).

Students wishing to take the exam to improve their grade must, in advance, request such an improvement from the academic services. If they wish, students can only improve their assessment in one part of the exam (correspondent to one test).

## 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: