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Wyszukujesz frazę "variance" wg kryterium: Temat


Wyświetlanie 1-4 z 4
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:
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:
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
    Wyświetlanie 1-4 z 4

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