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Displaying similar documents to “Information inequalities for the minimax risk of sequential estimators (with applications)”

Unbiased risk estimation method for covariance estimation

Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac (2014)

ESAIM: Probability and Statistics

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We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

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

Agata Boratyńska (2002)

Applicationes Mathematicae

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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.

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

Agata Boratyńska (2005)

Applicationes Mathematicae

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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.

Nonparametric bivariate estimation for successive survival times.

Carles Serrat, Guadalupe Gómez (2007)

SORT

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Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for...

Minimax and bayes estimation in deconvolution problem

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

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We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function where and is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Sequential estimation of powers of a scale parameter from delayed observations

Agnieszka Stępień-Baran (2009)

Applicationes Mathematicae

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The problem of sequentially estimating powers of a scale parameter in a scale family and in a location-scale family is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under a scale invariant loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.

Estimating quantiles with Linex loss function. Applications to VaR estimation

Ryszard Zieliński (2005)

Applicationes Mathematicae

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Sometimes, e.g. in the context of estimating VaR (Value at Risk), underestimating a quantile is less desirable than overestimating it, which suggests measuring the error of estimation by an asymmetric loss function. As a loss function when estimating a parameter θ by an estimator T we take the well known Linex function exp{α(T-θ)} - α(T-θ) - 1. To estimate the quantile of order q ∈ (0,1) of a normal distribution N(μ,σ), we construct an optimal estimator in the class of all estimators...