Institute of Measurement Science
Topic
Methods and algorithms for computing probability distributions of estimators and test statistics using characteristic functions
PhD. program
Applied mathematics
Name of the supervisor
Doc. RNDr. Viktor Witkovský, CSc.
Contact:
Receiving school
Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava
Annotation
Methods and algorithms will be developed in this dissertation to calculate the probability distributions of selected estimators and test statistics, as well as their applications. The focus will be on estimators (BLUE) and predictors (BLUP) in linear mixed models, particularly when there is a violation of standard assumptions regarding the normality distribution of errors and random effects. By assuming knowledge of the input variables' distribution or utilizing the observed empirical distribution, numerical methods that rely on the inversion of the characteristic function of the estimators and test statistics under consideration can be employed. The main objective of this dissertation is to devise efficient numerical methods and algorithms for computing the probability distribution of functions of random variables, which can be determined using characteristic functions. This encompasses a wide range of distributions that have practical applications in natural, technical, and biomedical sciences. The research is connected to two APVV projects, namely "Advanced mathematical and statistical methods for measurement and metrology" and "Effective computational methods for the characterization of materials at the nano scale," respectively. These projects will provide opportunities for international collaboration and active participation in significant domestic and foreign conferences. The completion of the dissertation will take place at the Institute of Measurement Science of the Slovak Academy of Sciences in Bratislava, in partnership with an external educational institution (EVI).