# Doc. RNDr. František Rublík, PhD.

Independent scientific worker IIa

Mail: umerrubl@savba.sk

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## Biography

In 1970 he finished his study at the Faculty of Science of Comenius University in Bratislava
in specialization mathematical statistics probability theory and became an employee of the Institute of Measurement Science of the Slovak Academy of Sciences in Bratislava. In 1973 he received the degree RNDr at the Comenius University in specialization probability theory and mathematical statistics.

He absolved postgraduate study at the Institute of Information and Automation of the Academy of Science of the Czech Republic in Prague and the degree CSc(PhD) he received in 1977.

In a large part of his research activities he dealt with the maximum likelihood principle with emphasis on its asymptotic properties from the testing point of view (optimality, parameters of non-centrality in general case, also for the Behrens-Fisher problem). Later his research focused on nonparametric statistical methods (tests based on ranks) and also on properties of
multivariate measures of location and spread.

He published also works on L-estimates, goodness-of-fit tests and characteristic roots of covariance matrices.

During his pedagogical activities at the Comenius University he delivered lectures on nonparametric methods and probability theory.

## The most important publications

Rublík, F.: On jackknifing the symmetrized Tyler matrix. Statistics 55(2021), 195–230.

Rublík, F.: Nonparametric Tests Applicable to High Dimensional Data. Austrian Journal of Statistics 48(2019), 14-42.

Rublík, F.: Estimates of the covariance matrix of vectors of U-statistics and confidence regions for vectors of Kendall’s tau. Kybernetika 52(2016) , 280 -293.

Rublík, F. and Somorčík, J.: On the Behrens–Fisher problem from the spatial median point of view. Journal of Statistical Computation and Simulation 85(2015), 3080–3091.

Rublík, F.: Nonparameric methods (in Slovak). Veda, vydavateľstvo Slovanskej akadémie vied, Bratislava 2011.

Rublík, F.: On testing hypotheses in the generalized Skillings-Mack random blocks setting.Kybernetika 47(2011), 657 – 677.

Rublík, F. and Somorčík, J.: Affine-equivariant spatial median and its use in the multivariate multi-sample location problem. Australian & New Zealand Journal of Statistics 53(2011), 197-215. & New Zealand

Rublík, F.: A Note on Simultaneous Confidence Intervals for Ratio of Variances. Communications in Statistics—Theory and Methods 39(2010), 1038–1045.

Bajla I., Rublík F., Arendacká B., Farkaš, I., Hornišová K., Štolc S. and Witkovský V.: Segmentation and supervised classification of image objects in Epo doping-control. Machine Vision and Applications 20(2009), 243–259.

Hönschová E. and Rublík F.: On asymptotic linearity of L-estimates. Mathematica Slovaca 59 (2009), 667–678.

Rublík, F.: Critical Values for Testing Location-Scale Hypothesis. Measurement Science review Volume 9 , 2009, Section 1, 9-15.

Rublík, F.: Asymptotic Local power of the LR test for some homogeneity hypotheses on normal distributions. Tatra Mountains Mathematical Publications 39(2008), 205–213.

Rublík, F.: On the asymptotic efficiency othe multisample location-scale rank tests and their adjustment for ties. Kybernetika 43(2007 ), 279–306.

Rublík, F.: The multisample version of the Lepage test. Kybernetika 41 (2005), 713 - 733.

Rublík, F.: Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions. Kybernetika 37 (2001), 61-78.

Rublík, F.: A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics. Applications of Mathematics 46 (2001), 339–351.

Rublík, F.: Asymptotic distribution of the likelihood ratio test statistic in the multisample case. Mathematica Slovaca, 49(1999), 577–598.

Rublík, F.: A quantile goodness-of-fit test applicable to distributions with non-differentiable densities. Kybernetika 33 (1997), 505-524.

Rublík, F.: On d-optimality of the LR tests. Kybernetika 31(1995), 189-206.

Rublík, F.: On consistency of the MLE. Kybernetika 31(1995), 45-64.

Rublík, F.: On Hodges-Lehmann optimality of LR tests. Kybernetika 30 (1994), 199-210.

Rublík, F.: On optimality of the LR tests in the sense of exact slopes. Part I. General Case. Kybernetika 25 (1989), 13-25.

Rublík, F.: On optimality of the LR tests in the sense of exact slopes. Part II. Application to Individual Distributions. 117-135.

Rublík, F.: On testing hypotheses approximable by cones. Mathematica Slovaca 39(1989), 199-213.

Rublík, F.: A note on the weak convergence of probability measures on C(K, L). Mathematica Slovaca 33 (1983), 133-139.