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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Robust m-estimator of parameters in variance components model

100%
Zmyślony R., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2002
|
tom 22
|
nr 1-2
61-71
EN
It is shown that a method of robust estimation in a two way crossed classification mixed model, recently proposed by Bednarski and Zontek (1996), can be extended to a more general case of variance components model with commutative a covariance matrices.
2
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Exact distribution for the generalized F tests

81%
Fonseca M., Mexia J., Zmyślony R.
Discussiones Mathematicae Probability and Statistics
|
2002
|
tom 22
|
nr 1-2
37-51
EN
Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate the p-values whenever they are available.
3
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Tests of independence of normal random variables with known and unknown variance ratio

81%
Gąsiorek E., Michalski A., Zmyślony R.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 2
233-247
EN
In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between this test and the classical t-test for independence of normal variables is shown. Moreover, the confidence interval for correlation coefficient is given. The results follow from the unified theory of testing hypotheses both for fixed effects and variance components presented in papers [6] and [7].
4
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Estimators and tests for variance components in cross nested orthogonal designs

81%
Fonseca M., Mexia J., Zmyślony R.
Discussiones Mathematicae Probability and Statistics
|
2003
|
tom 23
|
nr 2
175-201
EN
Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
5
Content available remote

Completeness for a family of normal distributions

60%
Zmyślony R.
Banach Center Publications
|
1980
|
tom 6
|
nr 1
355-357
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