Course guide of Multivariate Statistics (27011E1)

To properly follow this subject, it is recommended to have taken the core courses of the module Probability and Statistics

• Multivariate normal distribution: probabilistic aspects, characterizations
• Inference on the multivariate normal distribution: maximum-likelihood inference; distribution of the estimators. Hypothesis testing on mean vectors: Hotelling T2 methodology
• Principal component analysis
• Factor analysis
• Discriminant analysis
• Cluster analysis

• To handle with ease the multivariate normal distribution, as well as to know its main characteristics.
• To know and handle the mechanisms for estimation of the parameters of the multivariate normal distribution. Data applications.
• To know in depth the methodology derived from the application of the Hotelling T2 distribution to hypothesis testing on mean vectors. Application to more complex models such as Profile Analysis. Application to real data.
• To know the main characteristics of various Multivariate Analysis techniques: factorial techniques, canonical correlation, and classification and discrimination techniques.
• To know how to pose and recognise situations in which these techniques can be applied.
• To know how to solve specific cases by using some statistical software, and acquire skills in the elaboration of reports that expose the results derived from the application of the techniques to such cases.

SUBJECTS (THEORETICAL-PRACTICAL):

• Unit 1: Multivariate normal distribution
• Unit 2: Inference on the multivariate normal distribution
• Unit 3: Principal component analysis
• Unit 4: Factor analysis
• Unit 5: Discriminant analysis
• Unit 6: Cluster analysis

Development of practice consists of:

• Problem solving in classroom sessions
• Development of data analysis and simulation applications in laboratory sessions by using statistical software

• Anderson, T.W. (2003, 3rd ed.). An Introduction to Multivariate Statistical Analysis. John Wiley & Sons.
• Fujikoshi, Y., Ulyanov, V.V., and Shimizu, R. (2010). Multivariate Statistics. High-Dimensional and Large-Sample Approximations. John Wiley & Sons.
• Härdle, W.K., and Simar, L. (2015, 4th ed.). Applied Multivariate Statistical Analysis. Springer
• Izenman, A.J. (2013). Modern Multivariate Statistical Techniques. Regression, Classification, and Manifold Learning. Springer.
• Johnson, R.A., and Wichern, D.W. (1988). Applied Multivariate Analysis. Prentice Hall International, Inc.
• Rencher, A.C., and Christensen, W.F. (2012, 3rd ed.). Methods of Multivariate Analysis. John Wiley & Sons.
• Timm, N.H. (2002). Applied Multivariate Analysis. Springer.
• Tong, Y.L. (1990). The Multivariate Normal Distribution. Springer.

• Baillo, A., and Grané, A. (2008). 100 Problemas Resueltos de Estadística Multivariante. Delta Publicaciones.
• Hair, J., Anderson, R., Tatham, R., and Black, W. (2000, 5th ed.). Análisis Multivariante. Prentice Hall.
• Härdle, W.K., and Hlávka, Z. (2015, 2nd ed.). Multivariate Statistics. Exercises and Solutions. Springer.
• Tusell, F. (2016). Análisis Multivariante. (http://www.et.bs.ehu.es/~etptupaf/nuevo/ficheros/estad4/multi.pdf)
• Zelterman, D. (2015). Applied Multivariate Statistics with R. Springer.

• Prado 2 platform (https://prado.ugr.es)
• https://cran.r-project.org/
• https://rstudio.com/

• MD01. Lección magistral/expositiva 
• MD02. Sesiones de discusión y debate 
• MD03. Resolución de problemas y estudio de casos prácticos 
• MD04. Prácticas en sala de informática 
• MD06. Análisis de fuentes y documentos 
• MD07. Realización de trabajos en grupo 
• MD08. Realización de trabajos individuales 

Continuous evaluation of the course comprises the following aspects:

• Specific knowledge tests and oral/written exercise solving (45%)
• Individual and group works and seminars (45%)
• Participation, attitude, and personal effort (10%)

(Students undertaking activities and tests under the Continuous Evaluation process that constitute more that 50% of the weighted final qualification of the course will appear in the course report with the corresponding qualification mark.)

The extraordinary assessment will consist of a written exam including theoretical and practical questions about the subjects listed in this course guide. All students will have the possibility to obtain up to 100% of the qualification with this assessment.

The single final assessment established in the Normativa de evaluación y de calificación de los estudiantes de la Universidad de Granada will consist of a written exam including theoretical and practical questions about the subjects listed in this course guide. Students not taking this final exam will appear with the qualification "No Presentado". All students will have the possibility to obtain up to 100% of the qualification with this assessment.