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Objective Bayesian point and region estimation in location-scale models.

José M. Bernardo (2007)

SORT

Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this...

On a class of estimators in a multivariate RCA(1) model

Zuzana Prášková, Pavel Vaněček (2011)

Kybernetika

This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...

On a famous problem of induction.

José M. Bernardo (1985)

Trabajos de Estadística e Investigación Operativa

A Bayesian solution is provided to the problem of testing whether an entire finite population shows a certain characteristic, given that all the elements of a random sample are observed to have it. This is obtained as a direct application of existing theory and, it is argued, improves upon Jeffrey's solution.

On a robust significance test for the Cox regression model

Tadeusz Bednarski, Filip Borowicz (2006)

Discussiones Mathematicae Probability and Statistics

A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.

On a trivariate Poisson distribution

Sotirios Loukas, Evgenia H. Papageorgiou (1991)

Applications of Mathematics

A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined.

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 an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.

Elliott Nebenzahl (1984)

Trabajos de Estadística e Investigación Operativa

Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if...

On an estimation problem for type I censored spatial Poisson processes

Jan Hurt, Petr Lachout, Dietmar Pfeifer (2001)

Kybernetika

In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.

On Bayesian estimation in an exponential distribution under random censorship

Michal Friesl, Jan Hurt (2007)

Kybernetika

The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied...

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