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, with consultation, to be held on a single date, within the period provided for in the academic calendar, with a weight of 100% (students may choose to improve the grade correspondent to the 1st and/or 2nd tests, with the correspondent weight). Students must bring their laptops. The exam will last for 3 hours (2 hours for students improving the tests grades). Rated on a scale from 0 to 20 points.
Subject matter
Presentation of the Professor and the curricular unit
1. Introduction to R/RStudio
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
7. Classification and clustering analysis
7.1 Discriminant Analysis
7.2 Cluster Analysis
Programs
Programs where the course is taught: