Mathematical Statistics
A.Y. 2018/2019
Learning objectives
The main aim of the course is to introduce the basic concepts of Multivariate Mathematical Statistics, both from a theoretical and applied point of view. Some concepts of univariate mathematical statistics will be recalled and some modern techniques of Computational Statistics will be introduced. During the lab activities, the students will be trained to perform a data analysis with advanced software instruments (SAS and SAS Enterprise Miner).
Expected learning outcomes
Basic notions and theorems of Multivariate Mathematical and Computational Statistics.
The student will then be able to apply and broaden his/her knowledge of the subjects in different areas of interest, both in theoretical and applied contexts, and to perform statistical data analyses.
The student will then be able to apply and broaden his/her knowledge of the subjects in different areas of interest, both in theoretical and applied contexts, and to perform statistical data analyses.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Here an indication of the chapters that should be developed is provided.
The teachers could operate a selection due to lack of time.
1. Random vectors
2. The Multivariate Normal Distribution
2.1. Definition and properties of the multivariate normal distribution
2.2. Test for the normality of a random vector
2.3. Detection of outliers
3. Main multivariate distributions originating from the Normal
3.1. Wishart distribution
3.2. Hotelling T2 distribution
3.3. Wilks' Lambda distribution
4. Multivariate Hypothesis Tests
4.1. Test on one or two mean vectors
4.2. Multivariate Analysis of Variance (MANOVA)
4.3. Test on covariance matrices
5. Logistic regression
6. Principal component analysis (PCA)
7. Classification and regression trees (CART)
8. Discriminant Analysis and classification techniques
9. Factor Analysis
10. Computer Lab
Multivariate data analysis by statistical softwares (SAS and/or R)
The teachers could operate a selection due to lack of time.
1. Random vectors
2. The Multivariate Normal Distribution
2.1. Definition and properties of the multivariate normal distribution
2.2. Test for the normality of a random vector
2.3. Detection of outliers
3. Main multivariate distributions originating from the Normal
3.1. Wishart distribution
3.2. Hotelling T2 distribution
3.3. Wilks' Lambda distribution
4. Multivariate Hypothesis Tests
4.1. Test on one or two mean vectors
4.2. Multivariate Analysis of Variance (MANOVA)
4.3. Test on covariance matrices
5. Logistic regression
6. Principal component analysis (PCA)
7. Classification and regression trees (CART)
8. Discriminant Analysis and classification techniques
9. Factor Analysis
10. Computer Lab
Multivariate data analysis by statistical softwares (SAS and/or R)
MAT/06 - PROBABILITY AND STATISTICS - University credits: 9
Laboratories: 36 hours
Lessons: 42 hours
Lessons: 42 hours
Professors:
Aletti Giacomo, Fiori Anna Maria, Micheletti Alessandra
Professor(s)
Reception:
on appointment
office 2099