2018/2019

## Mathematical Statistics

Category 'Best Course for Career Development'

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'

Type:
Optional course (faculty)

Delivered by:
Faculty of Mathematics

When:
2 module

Language:
English

### Course Syllabus

#### Abstract

The main goal of mathematical statistics is adaptation of the theoretical probabilistic models to some practical problems in economics, physics, medicine, social sciences. Typically the precise distribution or random process that describes some phenomenon is not known; however, some information can be extracted from the series of observations or repeated experiments; this data is used to select the most appropriate model. We will discuss the most frequent classes of problems in this area, the parameters estimation and the hypothesis testing.

#### Learning Objectives

- To be competent in basic mathematical statistics: its notions, tools, general principles and possible applications in science and everyday life
- To know the restrictions in applications of standard statistical models

#### Expected Learning Outcomes

- Be competent in basic mathematical statistics
- Know the restrictions in applications of standard statistical models

#### Course Contents

- Basic mathematical statisticsNotions, tools, general principles and possible applications in science and everyday life
- The restrictions in applications of standard statistical models
- Statistical models, samples, descriptive statistics.Statistical models, samples, descriptive statistics. Empirical approach: empirical distribution and Glivenko – Cantelli theorem.
- Parametric statisticsParametric statistics: estimations and their main properties. Unbiased estimators. Efficient estimators. Cramer – Rao bound. Consistent estimators. Sufficient statistics and Fisher – Neumann factorization theorem. Rao – Blackwell theorem. Confidence intervals
- Statistical hypothesis testingStatistical hypothesis testing. Common test statistics. Null hypothesis statistical significance testing. Neumann – Pearson lemma and the most powerful test at the given significance level.

#### Assessment Elements

- Mixed exam (home + oral discussion)Studyings are given a home assignment, which should be submitted a few days before the exam. The exam is an oral discussion of the problems solved in the homework, and of the corresponding topics of the theory (the points given to each solution can be reduced in case of poor knowledge of statements and definitions used). The formula producing the final grade from the sum of points (rounding included) is published along with the assignment; a studying should solve approximately 70-80% of the assignment to achieve the grade «10», and 30–40% to achieve «4».
- Written home assignmentStudyings are given a home assignment, which should be submitted a few days before the exam. The exam is an oral discussion of the problems solved in the homework, and of the corresponding topics of the theory (the points given to each solution can be reduced in case of poor knowledge of statements and definitions used). The formula producing the final grade from the sum of points (rounding included) is published along with the assignment; a studying should solve approximately 70-80% of the assignment to achieve the grade «10», and 30–40% to achieve «4».

#### Interim Assessment

- Interim assessment (2 module)0.5 * Mixed exam (home + oral discussion) + 0.5 * Written home assignment

#### Bibliography

#### Recommended Core Bibliography

- Hogg, R. V., McKean, J. W., & Craig, A. T. (2014). Introduction to Mathematical Statistics: Pearson New International Edition. Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418145

#### Recommended Additional Bibliography

- Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756