1. SylabUZ
2. Faculty of Exact and Natural Sciences
3. winter term 2020/2021
4. computer science and econometrics - Second-cycle studies leading to MS degree
5. Multivariate Analysis

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Multivariate Analysis - course description

Aim of the course

Aim of the course is to familiarize students with statistical methods applied for analyzing multivariate data.

Prerequisites

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Passed lectures on: linear algebra, probability theory, mathematical statistics.

Scope

Lecture

1. Random vectors and its probability distributions. Multivariate normal distribution.          (4 hours)
2. Introduction to point estimation in multivariate models. (4 hours)
3. Fundamental sample distribution for multivariate normal model. (4 hours)
4. Hotelling’s T^2 distribution and its applications. (6 hours)
5. Principal components. (4 hours)
6. Analysis of canonical correlation. (4 hours)
7. Discriminant analysis. (4 hours)

               Class

1. Some elements form linear algebra used in multivariate statistical inferences. (4 hours)
2. The expectation and the covariance matrix under linear transformation. (2 hours)
3. Calculations of confidence areas and simultaneous confidence intervals. (4 hours)
4. Hotelling’s T^2 tests. (4 hours)
5. Test I. (2 hours)
6. Calculation of principal components. (4 hours)
7. Calculation of canonical variables. (4 hours)
8. Calculation of Bayesian classification rules. (4 hours)
9. Test II. (2 hours)

Teaching methods

Lecture traditional. Class - solving problems from prepared lists.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Recommended reading

1. D.F. Morrison, Wielowymiarowa analiza statystyczna, PWN, Warszawa, 1990
2. M. Krzyśko, Wielowymiarowa analiza statystyczna, UAM, Poznań, 2000

Further reading

M.S. Srivastava, C.G. Kathri, An introduction to multivariate statistics, North-Holland Pub., Amsterdam 1979.

Notes

Modified by dr hab. Stefan Zontek, prof. UZ (last modification: 20-10-2020 11:26)