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Home arrow Departments arrow Theoretical Methods arrow Department Projects arrow New methods of mathematical statistics
New methods of mathematical statistics

Project of the Scientific Grant Agency VEGA 2/0038/12

Duration of the project: 01/2012 - 12/2014

Principal investigator: Doc. RNDr.František Rublík, CSc..

Project partners: Faculty of Mathematics, Physics and Informatics of the Comenius University Bratislava (FMFI UK), Mathematical Institute SAS (MÚ SAV) and Institute of Measurement Science of the Slovak Academy of Sciences (ÚM SAV)

Project Summary

The aim of the project is the construction and the investigation of new methods for solving some actual problems of mathematical statistics. In the field of regression models (mixed models, nonlinear models or models withparametrized covariance matrix) new methods with generally applicable output will be developed. In addition, statistical methods aimed at the applications in measurement, design of experiment and biostatistical problemswill be constructed and investigated. Except for the procedures based on the classical assumption of normality of luctuations, the focus will be also on nonparametric methods not requiring this assumption, mainly for dealingwith problems in location and location-scale models, which will include also multivariate random fluctuations. We lso expect contributions to the theory of modern statistical methods in insurance, demography and linguistics.

The research of methods for inference on variance components in mixed linear models. Achieving new theoretical results on exact distribution of estimates or of test statistics for small sample sizes for normally distributed random effects and measurement errors in mixed linear models. Construction of confidence regions for parameters of mixed linear models and construction of tolerance intervals.

  • Development and investigation of statistical methods suitable for analysis of exhaled gases mainly based on data classification.
  • Construction of new procedures for statistical inference without the assumption of normality of distribution of random fluctuations. Research of nonparametric methods for hypotheses testing or construction of confidence intervals under general conditions of nonparametric type or under conditions on tails of distributions, in some cases also for multivariate distributions. Research into new procedures for high-dimensional data.
  • Construction of modification of the empirical likelihood aimed at obtaining a version applicable also in situations where difficulties occur until now and investigation of asymptotic properties of obtained procedures and investigation of models for interval data.
  • Development of new statistical methods and more efficient algorithms for optimization of experiments, above all for correlated observations of random processes, for nonlinear regression models and for multicriterial situations.
  • Development of statistical methods in insurance, models for population growth of society and conditioning of demographic phenomena.
  • Development of new methods in biostatistics, in particular in statistical shape analysis, with applications to biology and medicine.
  • Development and applications of statistical methods in linguistics.


Measurement Science Review (On-Line Journal)
Staff of Department of Theoretical Methods