A definition of generalized admissibility of Bayes estimates has been given. This generalized admissibility is a rule to identify whether Bayes estimates is acceptable or not under the condition of incorrect prior inf...A definition of generalized admissibility of Bayes estimates has been given. This generalized admissibility is a rule to identify whether Bayes estimates is acceptable or not under the condition of incorrect prior information. In this paper, a sufficient and necessary condition for the generalized admissibility is derived under quadratic loss. From this we can conclude that, when deviation of prior mean and deviation of prior variance do not go beyond the bound, the Bayes estimation is acceptable and it is discussed that how the deviation of the prior information influences on generalized admissibility. Because the precise distribution of prior information is unknown, the example gives a way to select the prior distribution. The example shows that this method is efficient and feasible.展开更多
Let Y have an n-variate normal distribution with covariance matrim σ2I and mean vector Xβ,where X is a known n×p matrix. The problem of estimating θ=σ2+β′X′CXβ is studied. The admissibility and inadmissib...Let Y have an n-variate normal distribution with covariance matrim σ2I and mean vector Xβ,where X is a known n×p matrix. The problem of estimating θ=σ2+β′X′CXβ is studied. The admissibility and inadmissibility of the estimators of the form bS2+β′X′CXβ, where β= (X′X) ˉX′Y and S2=(Y-Xβ)′(Y-Xβ), are established. Another class of admissible quadratic estimators of θ is derived.展开更多
基金Project supported by the Excellent Young Teachers Programof MOE of china
文摘A definition of generalized admissibility of Bayes estimates has been given. This generalized admissibility is a rule to identify whether Bayes estimates is acceptable or not under the condition of incorrect prior information. In this paper, a sufficient and necessary condition for the generalized admissibility is derived under quadratic loss. From this we can conclude that, when deviation of prior mean and deviation of prior variance do not go beyond the bound, the Bayes estimation is acceptable and it is discussed that how the deviation of the prior information influences on generalized admissibility. Because the precise distribution of prior information is unknown, the example gives a way to select the prior distribution. The example shows that this method is efficient and feasible.
文摘Let Y have an n-variate normal distribution with covariance matrim σ2I and mean vector Xβ,where X is a known n×p matrix. The problem of estimating θ=σ2+β′X′CXβ is studied. The admissibility and inadmissibility of the estimators of the form bS2+β′X′CXβ, where β= (X′X) ˉX′Y and S2=(Y-Xβ)′(Y-Xβ), are established. Another class of admissible quadratic estimators of θ is derived.
