Introduction to theoretical statistics

Subject description

  • Overview of descriptive statistics, basic graphical methods, examples.
  • Sampling, sampling design, sampling distribution, standard error, confidence intervals, examples. Demonstration of sampling distributions with simulations.
  • Definition and goal of statistical model, examples.
  • Parameter estimation, maximum likelihood method, estimator properties, asymptotical distributions, alternative methods for parameter estimations, examples.  Simulation examples, comparison of theoretical and empirical standard errors.
  • Hypotheses testing, test power, methods for test statistics, analysis of variance, independence tests, asymptotical properties, nonparametric tests, goodness of fit tests, examples. Empirical determination of power, simulation of tests, comparison of empirical and theoretical test statistic distributions.

The subject is taught in programs

Objectives and competences

The course presents the basic statistical ideas and their theoretical background. Theoretical concepts are illustrated on the examples of commonly used methods, tests and models.

At the end of the course, the student shall be able to present hiw problem theoretically, to choose the appropriate methods and to understand the results, assumptions and restrictions.

Teaching and learning methods

Lectures, labs, homeworks, seminarska naloga

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

Expected study results

Knowledge and understanding:

Understanding of the theoretical framework of the statistical ideas.

The course presents basic statistical ideas that form  the basis for all fields of statistics and overviews the most frequently used methods.

Basic sources and literature

  • Rice, J.A. (2007) Mathematical Statistics and Data Analysis. 3rd ed., Duxbury Press.
  • Roussas G.G. (1997) A course in mathematical statistics. 2 nd Ed. Academic Press.
  • Freedman, D, Pisani, R, Purves, R (1998) Statistics. New York, London: Norton.
  • Bickel, P, Doksum, K (1977) Mathematical Statistics: Basic Ideas and Selected Topics, New Jersey: Prentice Hall.
  • NIST Engineering Statistics Handbook,

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