*Conducted in terms:*2019L, 2020L

*Erasmus code:*14.3

*ISCED code:*0311

*ECTS credits:*5

*Language:*English

*Organized by:*Faculty of Economic Sciences

*Related to study programmes:*

# Mathematical Statistics 2400-PP2STa

1. Introduction: paradigm of Mathematical Staistics; mathematical models and empirical

inference.

2. Probability distributions and their empirical counterparts

3. Statistical models: families of probability distributions, parametric and nonparametric

models

4. Methods of estimation: the method of moments, maximum likelihood

5. Properties of estimators: bias, mean square error, Mimimum variance unbiased estimators,

Cramer-Rao inequality

6. Confidence intervals

7. Testing statistical hypotheses: test of significance, Neyman-Pearson lemma, most powerful

tests, typical parametric

and nonparametric tests

8.Selected special topics: e.g. Bayesian approach or introduction to multivariate analysis

## Type of course

## Course coordinators

## Learning outcomes

KNOWLEDGE

The student knows and understands selected concepts of probability calculus and mathematical statistics, the most important of which is a random variable, distribution of a random variable, basic characteristics of the distribution of a random variable and types of random variables. Knows the theory of statistical inference, point estimation, interval estimation, the theory of verification of statistical hypotheses. The student knows parametric and nonparametric models for verification of hypotheses regarding theoretical distribution.

SKILLS

The student is able to use the tools of mathematical statistics. He can use selected statistical procedures. Student is able to describe models in formal statistical language. The student is able to use analytical methods to correctly formulate and solve tasks in the field of mathematical statistics. The student is able to construct an unbiased and effective parameter estimator using the chosen method. The student is able to estimate the parameter using the confidence interval. He can verify the hypothesis regarding theoretical distribution.

COMMON SKILLS

The student knows the applications of theories and methods of mathematical statistics in economics and related sciences

## Assessment criteria

The student counts exercises (100%) based on 2 tests (60%), unannounced small tests (20%) and homework (20%), and the subject ends with a written exam. The final grade is 1/3 of the exercise grade + 2/3 of the exam grade.

## Bibliography

1. Michel Lavine, Statistical Thought, available online:

www.stat.duke.edu/~michael/book.html

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: