Methods and algorithms for exact probability distribution of the selected estimators and test statistics in linear mixed models and their applications

PhD study program: Applied Mathematics
Akademic year: 2022-2023
Advisor: doc. RNDr. Viktor Witkovský, CSc. (witkovsky@savba.sk)
External educational institution: Institute of Measurement Science SAS
Accepting university: Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics

Annotation:

The topic of the dissertation is focused on the development of methods and algorithms for calculating the probability distributions of estimators (BLUE), predictors (BLUP), and selected test statistics in linear mixed models in case of violation of standard assumptions about the normality distribution of errors and random effects. Assuming knowledge of the distribution of input variables, it will be possible to use methods based on numerical inversion of the characteristic function of the considered estimators and test statistics. The specific goal of the dissertation is the development of efficient numerical methods and algorithms for calculating the probability distribution of functions of random variables, which can be calculated using characteristic functions. It is a very wide class of divisions that find applications in various fields of natural, technical and biomedical sciences. The dissertation will be solved at the Institute of Measurement Science of the Slovak Academy of Sciences in Bratislava.

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