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Wyszukujesz frazę "coordinate free approach" wg kryterium: Temat


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Tytuł:
Testing hypotheses about structure of parameters in models with block compound symmetric covariance structure
Autorzy:
Zmyślony, Roman
Kozioł, Arkadiusz
Powiązania:
https://bibliotekanauki.pl/articles/1194457.pdf
Data publikacji:
2019-07-02
Wydawca:
Główny Urząd Statystyczny
Tematy:
coordinate-free approach
Jordan algebra
multivariate model
block compound symmetric covariance structure
best unbiased estimators
testing structure of mean vector
testing independence of block variables
Opis:
In this article we deal with testing the hypotheses of the so-called structured mean vector and the structure of a covariance matrix. For testing the above mentioned hypotheses Jordan algebra properties are used and tests based on best quadratic unbiased estimators (BQUE) are constructed. For convenience coordinate-free approach (see Kruskal (1968) and Drygas (1970)) is used as a tool for characterization of best unbiased estimators and testing hypotheses. To obtain the test for mean vector, linear function of mean vector with the standard inner product in null hypothesis is changed into equivalent hypothesis about some quadratic function of mean parameters (it is shown that both hypotheses are equivalent and testable). In both tests the idea of the positive and negative part of quadratic estimators is applied to get the test, statistics which have F distribution under the null hypothesis. Finally, power functions of the obtained tests are compared with other known tests like LRT or Roy test. For some set for parameters in the model the presented tests have greater power than the above mentioned tests. In the article we present new results of coordinate-free approach and an overview of existing results for estimation and testing hypotheses about BCS models.
Źródło:
Statistics in Transition new series; 2019, 20, 2; 139-153
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure and structured mean vector
Autorzy:
Kozioł, Arkadiusz
Powiązania:
https://bibliotekanauki.pl/articles/729718.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
best unbiased estimator
doubly exchangeable covariance structure
three-level multivariate data
coordinate free approach
structured mean vector
Opis:
In this article author obtain the best unbiased estimators of doubly exchangeable covariance structure. For this purpose the coordinate free-coordinate approach is used. Considered covariance structure consist of three unstructured covariance matrices for three-level $m-$variate observations with equal mean vector over v points in time and u sites under the assumption of multivariate normality. To prove, that the estimators are best unbiased, complete statistics are used. Additionally, strong consistency is proven. Under the proposed model the variances of the estimators of covariance components are compared with the ones in the model in [11].
Źródło:
Discussiones Mathematicae Probability and Statistics; 2016, 36, 1-2; 93-113
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-2 z 2

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