• New efficient statistical methods for comparisons evaluation

New efficient statistical methods for comparisons evaluation

Project: VEGA 1/0264/03

Investigators: M. Grendár, F. Rublík, A. Savin, V. Witkovský

The interlaboratory comparisons methods are important part of metrology in determination of the key reference value. An important question is how to determine the consensus value, also known as a comparison reference value (CRV), the associated uncertainty, in particular, the between-laboratory and the within-laboratory variance, and the confidence interval for the CRV. The interlaboratory experiments are frequently modeled by statistical mixed linear models, which include the fixed as well as the random effects. An unsolved problem in this setup was to find efficient estimators and/or tests for the parameters of the model, especially in the case of small sample sizes, i.e. if the number of laboratories and the number of repeated measurements is small. A new approach and the new interval estimators of the betweenlaboratory variance and of the comparison reference value were suggested and studied. The simulation study approved that the new methods perform better, especially in the case of small sample sizes. Further, the statistical properties of the goodness-of-fit tests for the Cauchy distribution and the nonparametric methods for multiple comparisons were studied and compared. It was shown that the new modified quantile test is better than the wellknown Henze test, especially for sample sizes less than 50. The method of Maximum Entropy (MaxEnt) is a valuable tool for inferring a probability distribution when only a limitted, insufficient information is available. New results were derived, concentrated on three interrelated issues pertinent to MaxEnt: probabilistic justification of the method, its place among statistical methods and limitations of applicability.

Publications:

• GRENDÁR, Marián Jr. - GRENDÁR, M. Chernoff`s bound forms. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering : 22nd international workshop. Melville, USA : AIP, 2003. P. 67- 72.
• RUBLÍK, František. On testing goodness-of-fit for Cauchy distribution. In Measurement Science Review. ISSN 1335-8871. Vol. 3, 2003, p. 49-52.
• SAVIN, Alexander - WIMMER, G. - WITKOVSKÝ, Viktor. On Kenward-Roger confidence intervals for common mean in interlaboratory trials. In Measurement Science Review. ISSN 1335-8871. Vol. 3, 2003, p. 53- 56.
• WIMMER, G. - WITKOVSKÝ, Viktor. Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model. In Journal of Statistical Computation and Simulation. ISSN 0094-9655. Vol. 73, no. 5, 2003, p. 333-346.