This paper considers the estimate problem on the mean matrix of mixture of normals. In order to evaluate estimators of the mean matrix, a fundamental frame of Φ-(general) decision problem is established. Under the fr...This paper considers the estimate problem on the mean matrix of mixture of normals. In order to evaluate estimators of the mean matrix, a fundamental frame of Φ-(general) decision problem is established. Under the frame, a class of Φ-minimax estimators are constructed.展开更多
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equation...In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.展开更多
In this paper Γ-minimax estimation of a multivariate normal mean under arbitrary squared error loss is considered where the covariance matrix of the normal distribution is a known symmetric and positive definite matr...In this paper Γ-minimax estimation of a multivariate normal mean under arbitrary squared error loss is considered where the covariance matrix of the normal distribution is a known symmetric and positive definite matrix with unknown multiple. The set F is fixed by imposing restrictions on the vector of first moments and on the matrix of second moments as well as on the first moment of the unknown factor determining of the covariance matrix. Necessary and sufficient conditions are derived which ensure that an estimator is Γ-minimax and that a prior is least favorable in Γ.展开更多
In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadr...In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.展开更多
文摘This paper considers the estimate problem on the mean matrix of mixture of normals. In order to evaluate estimators of the mean matrix, a fundamental frame of Φ-(general) decision problem is established. Under the frame, a class of Φ-minimax estimators are constructed.
文摘In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.
文摘In this paper Γ-minimax estimation of a multivariate normal mean under arbitrary squared error loss is considered where the covariance matrix of the normal distribution is a known symmetric and positive definite matrix with unknown multiple. The set F is fixed by imposing restrictions on the vector of first moments and on the matrix of second moments as well as on the first moment of the unknown factor determining of the covariance matrix. Necessary and sufficient conditions are derived which ensure that an estimator is Γ-minimax and that a prior is least favorable in Γ.
基金the National Natural Science Foundation of China(10271010)the Natural Science Foundation of Beijing(1032001)
文摘In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.
