Introduction to Mathematical Statistics
- 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
- Be competent in basic mathematical statistics
- Know the restrictions in applications of standard statistical models
- 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.
- Interim assessment (2 module)0.5 * Mixed exam (home + oral discussion) + 0.5 * Written home assignment
- 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
- 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