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1.
Minimax estimation of a cumulative distribution function by converting to a parametric problem 总被引:2,自引:1,他引:2
Let X = (X
1,...,X
n
) be a sample from an unknown cumulative distribution function F defined on the real line
. The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem
of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators
of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of
monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in
the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute
error. 相似文献
2.
In the present paper families of truncated distributions with a Lebesgue density
forx=(x
1,...,x
n
) ε ℝ
n
are considered, wheref
0:ℝ → (0, ∞) is a known continuous function andC
n
(ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator
form a saddle point when the parameter interval is sufficiently small. 相似文献