排序方式: 共有69条查询结果,搜索用时 31 毫秒
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Karine Bertin Nicolas Klutchnikoff 《Journal of statistical planning and inference》2011,141(7):2287-2297
In this paper, we are interested in the study of beta kernel density estimators from an asymptotic minimax point of view. These estimators allows to estimate density functions with support in [0,1]. It is well-known that beta kernel estimators are - on the contrary of classical kernel estimators - “free of boundary effect” and thus are very useful in practice. The goal of this paper is to prove that there is a price to pay: for very regular density functions or for certain losses, these estimators are not minimax. Nevertheless they are minimax for classical regularities such as regularity of order two or less than two, supposed commonly in the practice and for some classical losses. 相似文献
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Suppose a subset of populations is selected from k exponential populations with unknown location parameters θ1, θ2, …, θk and common known scale parameter σ. We consider the estimation of the location parameter of the selected population and the average worth of the selected subset under an asymmetric LINEX loss function. We show that the natural estimator of these parameters is biased and find the uniformly minimum risk-unbiased (UMRU) estimator of these parameters. In the case of k = 2, we find the minimax estimator of the location parameter of the smallest selected population. Furthermore, we compare numerically the risk of UMRU, minimax, and the natural estimators. 相似文献
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Summary:
In nonlinear statistical models, standard optimality functions for experimental
designs depend on the unknown parameters of the model. An appealing and robust
concept for choosing a design is the minimax criterion. However, so far, minimax optimal
designs have been calculated efficiently under various restrictive conditions only. We
extend an iterative relaxation scheme originally proposed by Shimizu and Aiyoshi (1980)
and prove its convergence under very general assumptions which cover a variety of situations
considered in experimental design. Application to different specific design criteria
is discussed and issues of practical implementation are addressed. First numerical results
suggest that the method may be very efficient with respect to the number of iterations
required.*Supported by a grant from the Deutsche Forschungsgemeinschaft. We are grateful to
a referee for his constructive suggestions. 相似文献
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In linear regression models, predictors based on least squares or on generalized least squares estimators are usually applied
which, however, fail in case of multicollinearity. As an alternative biased estimators like ridge estimators, Kuks-Olman estimators,
Bayes or minimax estimators are sometimes suggested. In our analysis the relative instead of the generally used absolute squared
error enters the objective function. An explicit minimax solution is derived which, in an important special case, can be viewed
as a predictor based on a Kuks-Olman estimator. 相似文献
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The problem of combining coordinates in Stein-type estimators, when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimator or to separate into groups and use separate shrinkage estimators on each group is considered. A Bayesian viewpoint is (of necessity) taken, and it is shown that the ‘combined’ estimator is, somewhat surprisingly, often superior. 相似文献
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D. Szatmari-Voicu 《统计学通讯:理论与方法》2013,42(5):709-721
We derive the AMSE (maximal asymptotic mean-squared-error) of the general class of L-estimators of scale that are location-scale equivariant and Fisher consistent. For non-normal error distributions, we determined estimators that have minimum AMSE over the subclass of (i) α-interquantile ranges and (ii) mixtures of at most two α-interquantile ranges. Finally, the L-estimators of scale symmetrized about the median were found to have the same AMSE as their nonsymmetrized counterparts, thus yielding the same results as in the symmetrized case. 相似文献
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Minimax Estimation of the Bounded Parameter of Some Discrete Distributions Under LINEX Loss Function
For a class of discrete distributions, including Poisson(θ), Generalized Poisson(θ), Borel(m, θ), etc., we consider minimax estimation of the parameter θ under the assumption it lies in a bounded interval of the form [0, m] and a LINEX loss function. Explicit conditions for the minimax estimator to be Bayes with respect to a boundary supported prior are given. Also for Bernoulli(θ)-distribution, which is not in the mentioned class of discrete distributions, we give conditions for which the Bayes estimator of θ ∈ [0, m], m < 1 with respect to a boundary supported prior is minimax under LINEX loss function. Numerical values are given for the largest values of m for which the corresponding Bayes estimators of θ are minimax. 相似文献
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Haifeng Xu 《统计学通讯:理论与方法》2013,42(12):2152-2164
In this article, we consider a heterogeneous preliminary test (HPT) estimator whose components are the OLS and feasible ridge regression (FRR) estimators, and derive the exact formulae for the moments of the HPT estimator using mathematical method. Since we cannot examine the MSE of the HPT estimator analytically, we execute the numerical evaluation to investigate the MSE performance of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Furthermore, using the minimax regret criterion proposed by Sawa and Hiromatsu (1973), we derive the optimal critical points of the preliminary F test. Our results show that the optimal significance points are greater than 19% and the optimal signicance points decrease as the denominator degrees of freedom of the preliminary F test statistic increases. 相似文献
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