Multivariate Statistics
Code
8518
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Filipe José Gonçalves Pereira Marques
Weekly hours
4
Teaching language
Português
Objectives
We want the student to become familiar with the Multivariate Normal and Wishart distributions and to acquire a solid knowledge about the main methods used in Multivariate Analysis, through a not too deep theoretical approach and the study of several applications and problems.
Prerequisites
Basic notions in Analysis and intermediate level knowledge in Linear Algebra, Probability and Statistics and Estimation.
Subject matter
1 – Brief review of basic notions in Linear Algebra
2 – The Multivariate Normal distribution. Maximum likelihood estimators and their distributions. The Wishart distribution
3 – Inference on mean vectors
3.1 – One sample tests
3.2 – Two sample tests – paired and independent samples
3.3 – Tests based on more than two samples
4 – Multivariate Regression and Canonical Analysis
5 – Principal Component Analysis and Factorial Analysis
6 – Discriminant Analysis and Classification
7 – Cluster analysis
Bibliography
Base reference:
Johnson, R. and Wichern, D. W. (2007), Applied Multivariate Statistical Analysis, 6th Edition, Prentice Hall, New Jersey
Complementary references:
Flury, B. (1997), A First Course in Multivariate Statistics, Springer. New York
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. (2002), Methods of Multivariate Analysis, John Wiley & Sons
Advanced references:
Anderson, T. W. (2003), An Introduction to Multivariate Statistical Analysis, 3rd ed., J.
Wiley & Sons, New York
Muirhead, R. J. (1982), Aspects of multivariate statistical theory, Wiley, New York
Kshirsagar, A. M. (1972). Multivariate Analysis, Dekker, New York
Teaching method
Classes/Labs where it is intended that, after the explanation of the topics, the students will take part in solving problems on those topics.
Evaluation method
There are three tests that can substitute the final exam in case of approval. Otherwise the student must do the final exam. More detailed rules are available in the Portuguese version.
If you require any further information, please feel free to contact regent (Prof. Filipe Marques).