Methods and algorithms for exact probability distribution of the selected estimators and test statistics and their applications

PhD study program: Applied Mathematics
Akademic year: 2023-2024
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 the calculation of probability distributions of selected estimators and test statistics and their applications, with a special emphasis on estimators (BLUE) and predictors (BLUP) 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 the input variables, or based on the observed empirical distribution, it will be possible to use methods based on the numerical inversion of the characteristic function of the considered estimators and test statistics. The specific goal of the dissertation is the development of effective numerical methods and algorithms for calculating the probability distribution of functions of random variables, which can be calculated using characteristic functions. This is a very broad class of distributions that find applications in various fields of natural, technical and biomedical sciences. The work is related to the solution of the scientific projects of APVV, MATHMER – “Advanced mathematical and statistical methods for measurement and metrology” and ECMeNaM “Effective computational methods for the characterization of materials at the nano scale”, which will enable the doctoral student to actively cooperate internationally and actively participate in important domestic and foreign conferences. The dissertation will be completed in a partner external educational institution (EVI), at the Institute of Measurement Science of the Slovak Academy of Sciences in Bratislava.

The aim of the dissertation is the development of methods and algorithms for the calculation of probability distributions of selected estimators and test statistics in models where there is a violation of standard assumptions about the normality of the distribution of errors.