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Modern methods of statistical inference based on maximum likelihood theory and its generalizations. Methods for
missing observations.
Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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To understand principles of advanced methods of statistical inference that are used in data analysis.
Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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The exercise class credit is necessary to sign up for the exam.
To get the credit for the exercise class the student needs to get 100 points from the assigned homework tasks. During the semester a number of homework assignments will be given. It will be indicated how many points the student can get for each assignment. In total, it is possible to get 140 points (or a few more). Solutions to homework assignments have to be delivered at the beginning of the exercise class (usually there is one week to work on the problem). No points are given to the solutions that are delivered after the deadline.
To get the exercise class credit it is needed:
• to obtain at least 100 points in total; and
• to solve correctly one indicated assignment.
Although in general one can skip some of the assignments, the indicated assignments (EM algorithm) are compulsory. For the compulsory assignment, sending an R-code (that works) is required. In case that a compulsory assignment is not solved correctly, there will be exactly one possibility to improve/correct your solution. No additional points are given for the corrected version.
The nature of these requirements precludes any possibility of additional attempts to obtain the exercise class credit.
Last update: Omelka Marek, doc. Ing., Ph.D. (02.12.2020)
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LEHMANN, E. L. and CASSELLA, G. (1998). Theory of point estimation. Springer, New York.
MCLACHLAN, G. J., KRISHNAN, T.: The EM Algorithms and Extensions, Wiley, 2008
Additional supporting literature: KOENKER, R.: Quantile regression. Cambridge university press, 2005.
LITTLE, R.J.A., RUBIN, D.B.: Statistical analysis with missing data. New York: John Wiley & Sons, 1987
PAWITAN, Y.: In all likelihood: statistical modelling and inference using likelihood. Oxford University Press, 2001.
SERFLING, R. J.: Approximation Theorems of Mathematical Statistics, Wiley, 1980.
VAN DER VAART, A. W.: Asymptotic statistics. Cambridge university press, 2000. Last update: Omelka Marek, doc. Ing., Ph.D. (03.12.2020)
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Lecture+exercises. Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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The exam will be organized as follows. First, an example will be given and there will be about 50 minutes to solve this example. After handing in this example, the student can make a short break, after which he/she gets two theoretical questions. To pass the exam, the student has to prove that he/she can solve the example as well as answer the theoretical questions in a satisfactory way.
The requirements for the oral exam are in agreement with the syllabus of the course as presented during lectures. Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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Clippings from the asymptotic theory - Delta Theorem and Moment Estimators
Theory of maximum likelihood
Profile, conditional and marginal likelihood
M-estimators and Z-estimators
Robust estimation
Quantile regression
EM-algorithm
Methods for missing data
Last update: Omelka Marek, doc. Ing., Ph.D. (11.12.2020)
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It is assumed that the students have already a very solid knowledge of statistics and probability theory. This is covered for instance by
Mukhopadhyay, N. (2000). Probability and statistical inference. CRC Press - almost the whole book except for Chapters 10 and 13 Khuri, A. I. (2009). Linear model methodology. Chapman and Hall/CRC - the knowledge of Chapters 1 - 6 is sufficient.
The students are prepared for the course if they pass the following courses: Mathematical Statistics 1 and 2 (NMSA331 and NMSA332), Probability Theory 1 (NMSA333), Linear regression (NMSA407). Last update: Omelka Marek, doc. Ing., Ph.D. (30.11.2020)
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