Mathematical Statistics - Seminar

Garant předmětu:

Tomáš Hobza

Lecturer:

Tutor:

Tomáš Hobza

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted to practical use of statistical methods studied in the course Mathematical Statistics 01MAS. The tutorial deals with calculation of Fisher information matrix of statistical models, finding unbiased estimators with minimal variance, parameter estimation by method of moments and method of maximum likelihood, derivation of critical regions for hypothesis testing using the Neyman-Pearson lemma and likelihood ratio, calculation of confidence intervals and non-parametric density estimation.

Requirements:

Basic course of Calculus and Probability (in the extent of the courses 01MAB3, 01MAB4 and 01MIP held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Transformations of random variables

2. Applications of the Law of large numbers nad the Central limit theorem

3. Calculation of Fisher information matrix of statistical models

4. Unbiased estimators with minimal variance

5. Parameter estimation by method of moments and method of maximum likelihood

6. Hypothesis testing using the Neyman-Pearson lemma

7. Likelihood ratio tests

8. Confidence intervals

9. Non-parametric density estimation

Syllabus of tutorials:

Study Objective:

Acquired knowledge: Basic statistical methods for estimation of parameters of statistical models and testing statistical hypothesis about parameters of models.

Acquired skills: Application of statistical models and corresponding methods to practical problems and real data analysis.

Study materials:

Compulsory literature:

[1] Shao J., Mathematical Statistics, Springer, 1999.

Optional literature:

[2] Lehmann E.L., Point Estimation, Wiley, N.Y., 1984.

[3] Lehmann E.L., Testing Statistical Hypotheses, Springer, N.Y., 1986.

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (elective course)
• Aplikované matematicko-stochastické metody (compulsory course in the program)