Project of the Scientific Grant Agency VEGA 1/3016/06

Duration of the project: 01/2006 - 12/2008

Principal investigator: Prof. RNDr. Andrej Pázman, DrSc. (FMFI UK, Bratislava)

Deputy: Doc. RNDr. František Rublík, CSc. (IMS SAS)

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

Financial support (IMS SAS): 103 000 SKK (2006)

Project Summary

The project focuses on some topical nonlinear tasks in statistical models. These include optimization of design of a nonlinear experiment, statistical inference in models with mixed (fixed and random) effects, in errors-in-variables models, studying the structure of nonlinear models and testing hypotheses in these models, development of new statistical methods aimed at applications in insurance, demography, linguistics, metrology and  biomedicine. The project is a direct continuation of the project VEGA 1/0264/03 „New nonlinear methods of mathematical statistics". The scientific goals of the project are:

• New methods for optimization of nonlinear regression experiments.
• New exact testing procedures in nonlinear models, as well as procedures for testing hypotheses in nonparametrical context. New estimators with regard to obtaining robustness as good as possible.
• New estimating and testing procedures in models with fixed and random parameters and in errors-in-variables models.
• Applicability of the two most important justifications of MaxEnt: the probabilistic justification (via the maximal probability method) and the statistical justification (via complementarity to maximum likelihood method), in models under nonlinear constraints. 
• Organization of the 5th international conference on mathematical statistics Probastat 2006.

Results

• There were prepared two manuscripts on tests of hypotheses on location and scale, based on ranks, that were submitted for publication to Journal of Nonparametric Statistics. The papers were returned for revision, which will be prepared within three months. Some partial results were published at the conference Prague Stochastics 2006.
• Methods for construction of approximate confidence intervals on a variance component in mixed linear models were investigated. A manuscript was prepared and submitted for publication to CC journal Kybernetika:
• ARENDACKÁ B.: A modification of the Hartung-Knapp interval on the variance component in two-variance-component models.
• A new iteration algorithm for estimation of parameters of the analysis function (the inverse of the calibration line) was proposed as well as a method for constructing an approximate confidence region for parameters of this line in situation when in a linear calibration problem we consider all regression variables in the model to be influenced by measurement errors.
• A method for computation of confidence intervals for the common mean value in key comparative interlaboratory studies was suggested.
  

Publications

• ARENDACKÁ, B.: O jednom intervalovom odhade pre variančný komponent. ODAM 2006, 7.9.-8.9.2006, Olomouc, ČR
• ARENDACKÁ, B.: Približné konfidenčné intervaly pre variančný komponent vo všeobecnom prípade modelu s dvomi komponentami. 14. zimní škola JČMF ROBUST 2006, Lhota nad Rohanovem 23.-27. ledna 2006. Poster.
• ARENDACKÁ, B.: Approximate and generalized approaches to confidence intervals on the variance components. PROBASTAT 2006. Fifth International Conference on Probability and Mathematical Statistics, June 5 - 9, 2006, Smolenice Castle, Slovak Republic. Prednáška.
• GRENDÁR M.: Trinity of conditional limit theorems. Fifth International Conference on Probability and Mathematical Statistics, June 5 - 9, 2006, Smolenice Castle, Slovak Republic. Poster.
• GRENDÁR, M.: Empirical Maximum Entropy Methods, in Bayesian inference and maximum entropy methods in science and engineering, A. Mohammad-Djafari (ed.), 419-425, AIP, Melville(NY), 2006.
• GRENDÁR, M.: Entropy and Effective Support Size, Entropy, 8/3, 169-174, 2006.
• GRENDÁR, M.: Criterion selection for Boltzmann Jaynes Inverse Problem: concluding considerations. Measurement Science Review, 6, 2006, 22-26.
• HORNIŠOVÁ, K.: Approximation of intrinsic curvature in one dimensional nonlinear regression model by moments of prior distribution of parameter. Measurement Science Review, 6, 2006, 40-49.
• HORNIŠOVÁ K.: Aproximácia vnútornej a parametrickej krivosti nelineárnych regresných modelov bez pouzitia derivácií. 14. zimní škola JČMF ROBUST 2006, Lhota nad Rohanovem 23.-27. ledna 2006. Poster.
• HORNIŠOVÁ K.: Optimal linearizations. Fifth International Conference on Probability and Mathematical Statistics, June 5 - 9, 2006, Smolenice Castle, Slovak Republic. Poster.
• RUBLÍK F.: On Testing the Hypothesis of Partial Common Principal Components, Proceedings Prague Stochastics 2006, pp 600-610.
• RUBLÍK F.: Asymptotic local power of the LR test for some homogeneity hypotheses on normal distributions. PROBASTAT 2006. Fifth International Conference on Probability and Mathematical Statistics, June 5 - 9, 2006, Smolenice Castle, Slovak Republic. Prednáška.
• WIMMER, G. - WITKOVSKÝ, V.: Scheffé-type confidence region for the calibration line. Austrian Journal of Statistics 35 (2-3), 2006, 397-406.
• WIMMER, G. - WITKOVSKÝ, V.: Univariate linear calibration via replicated errors-in-variables model. Journal of Statistcal Computation and Simulation, 2006. Accepted for publication.
• WITKOVSKÝ, V. - WIMMER G.: Exact and approximate confidence intervals for the comparison reference value. PROBASTAT 2006. Fifth International Conference on Probability and Mathematical Statistics, June 5 - 9, 2006, Smolenice Castle, Slovak Republic. Prednáška.
• WITKOVSKÝ, V. - WIMMER, G.: The weighted mid-P confidence interval for the difference of independent binomial proportions. In: Festschrift für Gabriel Altmann, Springer. Accepted for publication.
• WITKOVSKÝ, V.: Analýza dát pomocou lineárneho zmiešaného modelu. ROBUST 2006. Sborník prací 14. zimní školy JČMF ROBUST 2006, 23.-27. ledna 2006 ve Lhotě nad Rohanovem, JČMF Praha 2006, 387-402.