Sufficiency in linear models

Hilmar Drygas

Displaying similar documents to “Sufficiency in linear models”

Bad luck in quadratic improvement of the linear estimator in a special linear model

Gejza Wimmer (1998)

Applications of Mathematics

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The paper concludes our investigations in looking for the locally best linear-quadratic estimators of mean value parameters and of the covariance matrix elements in a special structure of the linear model (2 variables case) where the dispersions of the observed quantities depend on the mean value parameters. Unfortunately there exists no linear-quadratic improvement of the linear estimator of mean value parameters in this model.

Estimation of a quadratic function of the parameter of the mean in a linear model

Júlia Volaufová, Peter Volauf (1989)

Aplikace matematiky

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The paper deals with an optimal estimation of the quadratic function $β^{'} 𝐃 β$ , where $β \in ℛ^{k}, 𝐃$ is a known $k \times k$ matrix, in the model $𝐘, 𝐗 β, σ^{2} 𝐈$ . The distribution of $𝐘$ is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix $𝐗$ .

On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.

Jadwiga Kicinska-Slaby (1982)

Trabajos de Estadística e Investigación Operativa

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Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ^-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λ^b-1 e^-λx x^b-1 / Γ(b), x>0, where b is a known parameter, for loss function L(λ ^-r, λ^-r...

Uniformly best linear-quadratic estimator in a special structure of the regression model.

Wimmer, G. (1992)

Acta Mathematica Universitatis Comenianae. New Series

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Modified minimax quadratic estimation of variance components

Viktor Witkovský (1998)

Kybernetika

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The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

Locally best linear-quadratic estimators

Gejza Wimmer (1996)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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

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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...