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Infinitesimal robustness in Bayesian statistical models

100%

Boratyńska A.

Mathematica Applicanda

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1994

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tom 23

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nr 37

PL

.

EN

The problem of measuring the Bayesian robustness is considered. An upper bound for the oscillation of a posterior functional in terms of the Kolmogorov distance between the prior distributions is given. The norm of the Frechet derivative as a measure of local sensitivity is presented. The problem of finding optimal statistical procedures is presented.

2

Two-point priors and minimax estimation of a bounded parameter under convex loss

100%

Boratyńska A.

Applicationes Mathematicae

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2005

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tom 32

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nr 2

145-153

EN

The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

3

Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function

100%

Boratyńska A.

Applicationes Mathematicae

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2002

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tom 29

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nr 1

7-13

EN

The problem of posterior regret Γ-minimax estimation under LINEX loss function is considered. A general form of posterior regret Γ-minimax estimators is presented and it is applied to a normal model with two classes of priors. A situation when the posterior regret Γ-minimax estimator, the most stable estimator and the conditional Γ-minimax estimator coincide is presented.

4

Robust Bayesian estimation with asymmetric loss function

100%

Boratyńska A.

Applicationes Mathematicae

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2002

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tom 29

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nr 3

297-306

EN

The problem of robust Bayesian estimation in some models with an asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.

5

Concept of Robustness by Ryszard Zieliński. Robustness in Parametric Models

100%

Boratyńska A.

Mathematica Applicanda

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2012

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tom 40

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nr 2

PL

W działalnosci naukowej prof. dr hab. Ryszarda Zielinskiego obszernemiejsce zajmuje badanie zachowania sie procedur statystycznych przy zaburzeniu rozwazanego modelu statystycznego, czyli sytuacji, gdy obserwowana zmienna losowa nie spełnia załozen modelu. W tej czesci przedstawione zostana koncepcje i sposoby badania wrazliwosci procedur statystycznych, mierniki ich jakosci, metody wyznaczania procedur optymalnych i przykłady wykorzystania w róznych modelach rozwazanychw pracach Profesora.

EN

The concept of robustness of statistical procedures is one of the most important subject in Zielinski's papers. In this article the development of the idea of robustness as introduced in Zielinski's papers is presented. The definitions of a supermodel and a robustness function are given. The problem of the robust estimation of a scale parameter in an exponential model and the robustness of tests for comparison of means in two or more populations are described. Robustness in Bayesian statistical models is connected with an unexactly specified prior distribution. Here the following Zielinski's results in Bayesian robustness are presented: the most stable estimator in the Poisson model and the Bayes optimal stopping rule in a homogeneous Poisson process with conjugate classes of priors, the optimal experimental designs in Bayesian linear models under variation in the prior, an upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions. W działalnosci naukowej prof. dr hab. Ryszarda Zielinskiego obszerne miejsce zajmuje badanie zachowania sie procedur statystycznych przy zaburzeniu rozwazanego modelu statystycznego, czyli sytuacji, gdy obserwowana zmienna losowa nie spełnia załozen modelu. W tej czesci przedstawione zostana koncepcje i sposoby badania wrazliwosci procedur statystycznych, mierniki ich jakosci, metody wyznaczania procedur optymalnych i przykłady wykorzystania w róznych modelach rozwazanychw pracach Profesora.

6

Robust Bayesian estimation in a normal model with asymmetric loss function

64%

Boratyńska A., Drozdowicz M.

Applicationes Mathematicae

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1999

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tom 26

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nr 1

85-92

EN

The problem of robust Bayesian estimation in a normal model with asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ-minimax estimators are constructed. The situations when those estimators coincide are presented.

7

Bayes robustness via the Kolmogorov metric

64%

Boratyńska A., Zieliński R.

Applicationes Mathematicae

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1993-1995

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tom 22

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nr 1

139-143

EN

An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.

Ograniczanie wyników

5 Applicationes Mathematicae

2 Mathematica Applicanda

7 Boratyńska A.

1 Drozdowicz M.

1 Zieliński R.

1 2012

1 2005

2 2002

1 1999

1 1994

1 1993

Infinitesimal robustness in Bayesian statistical models

Two-point priors and minimax estimation of a bounded parameter under convex loss

Posterior regret Γ-minimax estimation in a normal model with asymmetric loss function

Robust Bayesian estimation with asymmetric loss function

Concept of Robustness by Ryszard Zieliński. Robustness in Parametric Models

Robust Bayesian estimation in a normal model with asymmetric loss function

Bayes robustness via the Kolmogorov metric