Selected Results of Basic Research |
- Generalized confidence intervals for the variance component and new multisample nonparametric tests based on ranks
Generalized confidence intervals for the variance component and new multisample nonparametric tests based on ranks
Projects:VEGA 1/0264/03 and VEGA 2/4026/04
Investigators: B. Arendacká, F. Rublík
New generalized interval estimators for the variance component corresponding to the random factor in mixed linear models with two variance components were proposed. Statistical properties of the new interval estimators were explored through simulation for a wide class of experimental designs with respect to their probability of coverage of the true, but unknown estimated parameter of variance(the variance component) and their expected length.
A multisample version of Lepage test based on ranks was proposed. The proof that the proposed test is asymptotically chi-square distributed under the null hypothesis and the derivation of its parameter of noncentrality in case of Pitman alternatives can be regarded as important theoretical results. It was proved that for normal distribution the asymptotic efficiency of the test with respect to the likelihood ratio statistic is 61%-95%, according to the nature of Pitman alternative.
Also, a new nonparametric rule for multiple comparisons based on ranks permitting unequally sized samples from populations compared was constructed. Properties of nonparametric methods for multiple comparisons based on joint ranks as well as ranks obtained by pairwise ranking were explored by means of simulation.
Publications:
- Arendacká, B. (2005). Generalized confidence intervals on the variance component in mixed linear models with two variance components. Statistics, Vol. 39, No.4, 275-286.
- Rublík, F. (2005). The multisample version of the Lepage test. Kybernetika, Vol. 41, No. 6, 695 – 716.
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