Subject description
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Overview of probability.
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Sampling, sampling distribution, standard error, confidence intervals.
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Statistical models, formulation of models, parameters, examples of models, the significance of models for data analysis, forecasting, limitations of statistical models.
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Parameter estimation. Methods for parameter estimation, standard errors, asymptotic properties of estimators, optimality.
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Hypothesis testing, test statistics and their distributions, likelihood ratio test, asymptotic properties of tests, Neyman’Person lemma, optimal tests, analysis of variance.
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Linear regression, assumptions of linear regression, least squares method, Gauss-Markov theorem, forecasting, general linear hypothesis, diagnostic methods, generalizations of regression models.
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Nonparametric methods, nonparametric hypothesis tests, Comparison to classical hypothesis tests.
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Models of time series, ARIMA models, parameter estimates, hypothesis tests.
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Simulation, random number generation, generation of a given distribution, bootstrap, jack-knife, limitations of simulations.
The subject is taught in programs
Objectives and competences
Applications of statistics are based on a collection of fundamental ideas. The purpose of the course is to systematically present the fundamental chapters of statistics with emphasis on the theoretical basis for various applications. The acquired knowledge is a starting point for independent work in statistics.
Teaching and learning methods
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Lectures.
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Homework with data analysis examples.
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Seminar assignment with more demanding problems including data analysis and simulation.
Expected study results
Understanding statistical concepts at the level of doctoral studies to a degree where students will be able to embark on independent research in their respective fields.
Basic sources and literature
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Rice, J.A. (1995) Mathematical Statistics and Data Analysis. 3rd.ed., Duxbury Press.
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Weisberg, S. (1985) Applied Linear Regression. 2nd Ed., John Wiley & Sons.
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Rousas G.G. (1997) A course in mathematical statistics. 2 nd Ed. Academic Press.
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F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä, L. E. Meester, A Modern Introduction to Probability and Statistics, Springer, 2005.
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D. R. Cox, D. V. Hinkley, Theoretical statistics, Chapman & Hall/CRC, 2000.
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C. Chatfield, The analysis of time series: an introduction, 6th ed. Chapman & Hall/CRC, 2004.K.V. Mardia, J.T. Kent in J.M. Bibby: Multivariate analysis. Academic Press, London, 1989.
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