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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Exact distribution for the generalized F tests

100%
Fonseca M., Mexia J., Zmyślony R.
Discussiones Mathematicae Probability and Statistics
|
2002
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tom 22
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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.
2
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Estimators and tests for variance components in cross nested orthogonal designs

100%
Fonseca M., Mexia J., Zmyślony R.
Discussiones Mathematicae Probability and Statistics
|
2003
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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.
3
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Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models

88%
Michalski A.
Discussiones Mathematicae Probability and Statistics
|
2009
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tom 29
|
nr 1
5-29
EN
The paper deals with construction of exact confidence intervals for the variance component σ₁² and ratio θ of variance components σ₁² and σ² in mixed linear models for the family of normal distributions $𝒩_t(0, σ₁²W + σ²I_t)$. This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ₁², σ²) for: 1) the variance components ratio θ - built by using test statistics obtained from the decomposition of a quadratic form y'Ay for the Bayes locally best estimator of σ₁², Michalski and Zmyślony (1996), 2) the variance component σ₁² - constructed using Bayes point estimators from BIQUE class (Best Invariant Quadratic Unbiased Estimators, see Gnot and Kleffe, 1983, and Michalski, 2003). In the paper an idea of construction of confidence intervals using generalized p-values is also presented (Tsui and Weerahandi, 1989, Zhou and Mathew, 1994). Theoretical results for Bayes interval estimators and for some generalized confidence intervals by simulations studies for some experimental layouts are illustrated and compared (cf Arendacká, 2005).
4
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On the General Gauss-Markov Model for Experiments in Block Designs

75%
Caliński T.
Biometrical Letters
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2012
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tom 49
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nr 1
1-36
EN
The main estimation and hypothesis testing results related to the Gauss- Markov model, in its general form, are recalled and the application of these results to the analysis of experiments in block designs is considered. Special attention is given to the randomization-derived model for a general block design, and for a proper block design in particular. The question whether the randomization-derived model can be considered as a particular general Gauss-Markov model is discussed. It is indicated that the former, as a mixed model, is in fact an extension of the general Gauss-Markov model. Thus, the analysis based on the randomization-derived model requires a more extended methodical approach. The present paper has been inspired by one of the last papers of Professor Wiktor Oktaba.
5
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On a New Approach to the Analysis of Variance for Experiments with Orthogonal Block Structure.

75%
Calinski T., Siatkowski I.
Biometrical Letters
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2017
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tom 54
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nr 2
91-122
EN
Summary The main estimation and hypothesis testing results are presented for experiments conducted in proper block designs. It is shown that, under appropriate randomization, these experiments have the convenient orthogonal block structure. Because of this, the analysis of experimental data can be performed in a comparatively simple way. Certain simplifying procedures are introduced. The main advantage of the presented methodology concerns the analysis of variance and related hypothesis testing procedures. Under the adopted approach one can perform them directly, not by combining results from intra-block and inter-block analyses. Application of the theory is illustrated by three examples of real experiments in proper block designs. This is the first of a projected series of papers concerning the analysis of experiments with orthogonal block structure.
6
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The use of outlier detection methods in the log-normal distribution for the identification of atypical varietal experiments

75%
Kornacki A., Bochniak A.
Biometrical Letters
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2015
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tom 52
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nr 2
75-84
EN
In this study the Akaike information criterion for detecting outliers in a log-normal distribution is used. Theoretical results were applied to the identification of atypical varietal trials. This is an alternative to the tolerance interval method. Detection of outliers with the help of the Akaike information criterion represents an alternative to the method of testing hypotheses. This approach does not depend on the level of significance adopted by the investigator. It also does not lead to the masking effect of outliers.
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