MULTIVARIATE STATISTICS
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2015/2016
- Teacher
- JOSEF ESCHGFALLER
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- MAT/06
Training objectives
- Students learn first the difficulties of
statistics in high dimensions (curse of
dimensionality). Then we deal with
linear regression (simple and multivariate)
and the linear correlation coefficient,
together with a critical review of the
limits of linear models.
The students learn then how the theory
of symmetric linear operators and the
properties of the Rayleigh quotient
are used in principal component analysis.
The utility of graphical representations
is illustrated with many figures in the
case of 15 Italian towns.
In the last part, dedicated to cluster
analysis, we begin with a discussion of
genetic algorithms. In a chapter on
non archimedean metrics the students
may appreciate the practical utility of a
construction born in pure mathematics. Prerequisites
- Linear algebra.
Course programme
- Difficulties in higher dimension (3 hours).
Mean and variance (3 hours).
Simple linear regression (3 hours).
Critics (2 hours).
Simple linear regression in matricial
form (1 hour).
Multivariate linear regression (2 hours).
Rayleigh quotient (3 hours).
Lines of orthogonal regression (4 hours).
Relative maxima and minima of the
Rayleigh quotient (3 hours).
Principal components (4 hours).
Graphical representations (2 hours).
Genetic algorithms (2 hours).
Non archimedean metrics (4 hours).
Cluster analysis (3 hours). Didactic methods
- Frontal lectures.
Learning assessment procedures
- Oral examination.
Reference texts
- Although not necessary for the exam, the
following books could be useful for
a deeper autonomous study.
B. Flury: A first course in multivariate statistics. Springer 1997.
A. Rizzi: Analisi dei dati. NIS 1985.
K. Mardia/J. Kent/J. Bibby: Multivariate analysis. Academic Press 2000.
J. Gentle: Elements of computational statistics. Springer 2002.
I. Jolliffe: Principal component analysis. Springer 2002.
