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On a distance between estimable functions.

Concepción Arenas Solá (1989)

Qüestiió

In this paper we study the main properties of a distance introduced by C.M. Cuadras (1974). This distance is a generalization of the well-known Mahalanobis distance between populations to a distance between parametric estimable functions inside the multivariate analysis of variance model. Reduction of dimension properties, invariant properties under linear automorphisms, estimation of the distance, distribution under normality as well as the interpretation as a geodesic distance are studied and...

On admissibility of linear estimators in models with finitely generated parameter space

Ewa Synówka-Bejenka, Stefan Zontek (2016)

Kybernetika

The paper refers to the research on the characterization of admissible estimators initiated by Cohen [2]. In our paper it is proved that for linear models with finitely generated parameter space the limit of a sequence of the unique locally best linear estimators is admissible. This result is used to give a characterization of admissible linear estimators of fixed and random effects in a random linear model for spatially located sensors measuring intensity of a source of signals in discrete instants...

On conditional independence and log-convexity

František Matúš (2012)

Annales de l'I.H.P. Probabilités et statistiques

If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.

On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters

Konrad Neumann, Stefan Zontek (2006)

Discussiones Mathematicae Probability and Statistics

We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of...

On small sample inference for common mean in heteroscedastic one-way model

Viktor Witkovský, Alexander Savin, Gejza Wimmer (2003)

Discussiones Mathematicae Probability and Statistics

In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward...

On some properties of ML and REML estimators in mixed normal models with two variance components

Stanisław Gnot, Andrzej Michalski, Agnieszka Urbańska-Motyka (2004)

Discussiones Mathematicae Probability and Statistics

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 𝒩 {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...

On testing variance components in unbalanced mixed linear model

Lýdia Širková, Viktor Witkovský (2001)

Applications of Mathematics

The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.

On variance of the two-stage estimator in variance-covariance components model

Júlia Volaufová (1993)

Applications of Mathematics

The paper deals with a linear model with linear variance-covariance structure, where the linear function of the parameter of expectation is to be estimated. The two-stage estimator is based on the observation of the vector Y and on the invariant quadratic estimator of the variance-covariance components. Under the assumption of symmetry of the distribution and existence of finite moments up to the tenth order, an approach to determining the upper bound for the difference in variances of the estimators...

Optimization of the size of nonsensitiveness regions

Eva Lešanská (2002)

Applications of Mathematics

The problem is to determine the optimum size of nonsensitiveness regions for the level of statistical tests. This is closely connected with the problem of the distribution of quadratic forms.

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