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On Fourier coefficient estimators consistent in the mean-square sense

Waldemar Popiński (1994)

Applicationes Mathematicae

The properties of two recursive estimators of the Fourier coefficients of a regression function f ∈ L 2 [ a , b ] with respect to a complete orthonormal system of bounded functions (ek) , k=1,2,..., are considered in the case of the observation model y i = f ( x i ) + η i , i=1,...,n , where η i are independent random variables with zero mean and finite variance, x i ∈ [ a , b ] ⊂ R 1 , i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors η i , i=1,...,n . Unbiasedness and mean-square...

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 maximum likelihood estimation in mixed normal models with two variance components

Mariusz Grządziel (2014)

Discussiones Mathematicae Probability and Statistics

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.

On non-nested regression models

Jiří Anděl (1993)

Commentationes Mathematicae Universitatis Carolinae

A generalization of a test for non-nested models in linear regression is derived for the case when there are several regression models with more regressors.

On one approach to local surface smoothing

Nikolay Dikoussar, Csaba Török (2007)

Kybernetika

A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.

On parameter-effects arrays in non-linear regression models

Rastislav Potocký, Van Ban To (1993)

Applications of Mathematics

Formulas for a new three- and four-dimensional parameter-effects arrays corresponding to transformations of parameters in non-linear regression models are given. These formulae make the construction of the confidence regions for parameters easier. An example is presented which shows that some care is necessary when a new array is computed.

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 alternative forms equivalent to Kruskal's condition for OLSE to be BLUE.

Gabriela Beganu (2007)

RACSAM

The necessary and sufficient condition for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the expected mean in the general univariate linear regression model was given by Kruskal (1968) using a coordinate-free approach. The purpose of this article is to present in the same manner some alternative forms of this condition and to prove two of the Haberman’s equivalent conditions in a different and simpler way. The results obtained in the general univariate...

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 hypotheses in the generalized Skillings-Mack random blocks setting

František Rublík (2011)

Kybernetika

The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...

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.

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