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    Wyświetlanie 1-12 z 12
    Tytuł:
    On maximum likelihood estimation in mixed normal models with two variance components
    Autorzy:
    Grządziel, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/729796.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variance component
    linear mixed model
    maximum likelihood
    Opis:
    In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2014, 34, 1-2; 187-197
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on the existence of the maximum likelihood estimate in variance components models
    Autorzy:
    Grządziel, Mariusz
    Michalski, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/729792.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variance component
    linear mixed model
    maximum likelihood
    Opis:
    In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2014, 34, 1-2; 159-167
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some constructions of nested balanced equireplicate block designs
    Autorzy:
    Rai, Shivani
    Banerjee, Shakti
    Kageyama, Sanpei
    Powiązania:
    https://bibliotekanauki.pl/articles/729854.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Balanced incomplete block (BIB) design
    efficiency balanced (EB) design
    variance balanced (VB) design
    efficiency balanced ternary (EBT)
    variance balanced ternary (VBT)
    efficiency balanced quaternary (EBQ)
    variance balanced quaternary (VBQ)
    Opis:
    arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2003, 23, 1; 45-68
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    ANOVA using commutative Jordan algebras, an application
    Autorzy:
    Rodrigues, Paulo
    Mexia, João
    Powiązania:
    https://bibliotekanauki.pl/articles/729984.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    commutative Jordan algebras
    variance components
    orthogonal models
    ANOVA
    Opis:
    Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2006, 26, 2; 179-191
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cross additivity - an application
    Autorzy:
    Ferreira, Sandra
    Ferreira, Dário
    Mexia, João
    Powiązania:
    https://bibliotekanauki.pl/articles/730004.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    cross nested designs
    cross additivity
    variance components
    UMVUE
    Opis:
    We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility arises from the introduction of the concept of regions of controled posterior risk.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2006, 26, 2; 207-219
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Variance components estimation in generalized orthogonal models
    Autorzy:
    Fernandes, Célia
    Ramos, Paulo
    Ferreira, Sandra
    Mexia, João
    Powiązania:
    https://bibliotekanauki.pl/articles/729930.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    generalized orthogonal models
    variance components
    generalized cross nesting designs
    Opis:
    The model $y = ∑_{j=1}^w X_j β̲_j + e̲$ is generalized orthogonal if the orthogonal projection matrices on the range spaces of matrices $X_j$, j = 1, ..., w, commute. Unbiased estimators are obtained for the variance components of such models with cross-nesting.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2007, 27, 1-2; 99-115
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Selective generalized F tests
    Autorzy:
    Nunes, C.
    Mexia, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/729760.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed linear models
    variance components
    generalized polar coordinates
    selective F testes
    Opis:
    Generalized F tests were introduced by Michalski and Zmyślony (1996) for variance components and later (1999) for linear functions of parameters in mixed linear models. We now use generalized polar coordinates to obtain, for the second case, tests that are more powerful for selected families of alternatives.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2004, 24, 2; 281-288
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models
    Autorzy:
    Michalski, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/729664.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed linear models
    variance components
    hypothesis testing
    confidence intervals
    generalized p-values
    Opis:
    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 $_t(0, σ₁²W + σ²I_t)$. 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).
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2009, 29, 1; 5-29
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algebraic structure for the crossing of balanced and stair nested designs
    Autorzy:
    Fernandes, Célia
    Ramos, Paulo
    Mexia, João
    Powiązania:
    https://bibliotekanauki.pl/articles/729814.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    balanced nested designs
    stair nested designs
    crossing
    commutative Jordan algebras
    variance components
    inference
    Opis:
    Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2014, 34, 1-2; 71-88
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tests of independence of normal random variables with known and unknown variance ratio
    Autorzy:
    Gąsiorek, Edward
    Michalski, Andrzej
    Zmyślony, Roman
    Powiązania:
    https://bibliotekanauki.pl/articles/729874.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed linear models
    variance components
    correlation
    quadratic unbiased estimation
    testing hypotheses
    confidence intervals
    Opis:
    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].
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2000, 20, 2; 233-247
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some properties of ML and REML estimators in mixed normal models with two variance components
    Autorzy:
    Gnot, Stanisław
    Michalski, Andrzej
    Urbańska-Motyka, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/729742.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed linear models
    likelihood-based inference
    ML- and REML- estimation
    variance components
    Fisher's information
    Opis:
    In the paper, the problem of estimation of variance components σ₁² and σ₂² by using the ML-method and REML-method in a normal mixed linear model {Y,E(Y) = Xβ, Cov(Y) = σ₁²V + σ₂²Iₙ} is considered. This paper deal with properties of estimators of variance components, particularly when an explicit form of these estimators is unknown. The conditions when the ML and REML estimators can be expressed in explicit forms are given, too. The simulation study for one-way classification unbalanced random model together with a new proposition of approximation of expectation and variances of ML and REML estimators are shown. Numerical calculations with reference to the generalized Fisher's information are also given.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2004, 24, 1; 109-126
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algebraic structureof step nesting designs
    Autorzy:
    Fernandes, Célia
    Ramos, Paulo
    Mexia, João
    Powiązania:
    https://bibliotekanauki.pl/articles/729913.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    commutative Jordan algebras
    cartesian product of commutative Jordan algebras
    step nesting
    variance components
    UMVUE
    Opis:
    Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce the cartesian product of commutative Jordan algebras.
    Źródło:
    Discussiones Mathematicae Probability and Statistics; 2010, 30, 2; 221-235
    1509-9423
    Pojawia się w:
    Discussiones Mathematicae Probability and Statistics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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