2020/2021

Introduction to Mathematical Statistics

Category 'Best Course for Career Development'

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

Category 'Best Course for New Knowledge and Skills'

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 1, 2 module

Instructors: Alexey Vladimirovich Klimenko, Alexandra Skripchenko

Language: English

ECTS credits: 3

Contact hours: 40

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 statistics
  Notions, 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 statistics
  Parametric 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 testing
  Statistical 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)
• Written home assignment

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