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Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant | σ 2 | in the MGM model ( U , X B , σ 2 V ) , > 0 , scalar σ 2 > 0 , with a matrix V 0 . A known n × p random matrix U has the expected value E ( U ) = X B , where the n × d matrix X is a known matrix of an experimental design, B is an unknown d × p matrix of parameters and σ 2 V is the covariance matrix of U , being the symbol of the Kronecker...

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

Gejza Wimmer (1998)

Applications of Mathematics

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.

Bayes and empirical bayes tests for the life parameter

Lichun Wang (2005)

Applicationes Mathematicae

We study the one-sided testing problem for the exponential distribution via the empirical Bayes (EB) approach. Under a weighted linear loss function, a Bayes test is established. Using the past samples, we construct an EB test and exhibit its optimal rate of convergence. When the past samples are not directly observable, we work out an EB test by using the deconvolution kernel method and obtain its asymptotic optimality.

Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior

Marek Męczarski, Ryszard Zieliński (1997)

Applicationes Mathematicae

A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.

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