Selected Topics in Mathematical Statistics

Subject description

Basics of mathematical statistics:
Core topics: Order Statistics. Sufficiency, completeness and unbiasedness. Point estimation. Hypotheses testing. Sequential procedures. Confidence regions. The maximum likelihood method. Least square estimators. Analysis of variance.

Bayesian methods in statistics:
Core topics: Single-parameter models, multi-parameter models and connections to standard statistical methods. Hierarchical models. Model checking and sensitivity analysis. Study design in Bayesian analysis. Introduction to regression models.

Optional topics: Multiple testing problem. Approximation based on posterior models. Posterior simulation. Markov chain simulation. Other specific models of Bayesian data analysis.

Mathematical methods in econometrics:
Core topics: Linear and nonlinear regression. Heteroskedasticity and autocorrelation.

Stochastic processes:
Core topics: Markov chains. Renewal processes. Point processes. Continuous time Markov chains. Brownian motion.

The subject is taught in programs

Objectives and competences

State-of-the-art developments in the field of mathematical statistics and specific methods used in data analysis, especially Bayesian methods in statistics, mathematical methods in econometrics and stochastic processes.

Comprehensive overview of the field, supplemented by methods of the specialization in question. The qualification of students for research and guidance of their work on the PhD thesis.

Teaching and learning methods

Lectures, exercises, homeworks, projects, self-study of literature, consultations.

Expected study results

Knowledge and understanding:

Advanced methods of mathematical statistics. Individual work of the student emphasizes the areas of their PhD thesis.

Basic sources and literature

  • G. G. Roussas. A course in mathematical statistics. Academic Press, 2nd edition, 1997.
  • A. Gelman, J.B.Carlin, H.S. Stern, D.B. Rubin: Bayesian Data Analysis. Chapman&Hall, 1995.
  • M. Verbeek: A guide to modern econometrics, 2004.
  • M. Hatanaka: Time-series based econometrics – Unit roots and cointegration, 1996.
  • P. J. Brockwell, R. A. Davis: Time series : Theory and methods, 2006.
  • S. I. Resnick: Adventures in stochastic processes, 1992.

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