A Unified and Broadened Class of Admissible Minimax Estimators of a Multivariate Normal Mean

The problem of estimating the mean of a multivariate normal distribution is considered. A class of admissible minimax estimators is constructed. This class includes two well-known classes of estimators, Strawderman's and Alam's. Further, this class is much broader than theirs.     

A minimax optimal control problem

A control system x=f(t,x,u) is considered, and a cost functional ess supT ₀tT ₁ G(t, x(t),u(t)) is to be minimized. Necessary conditions for optimality (maximum principle and transversality conditions) are derived. It is also shown that an optimal control is optimal for the corresponding problem on a subinterval of [T ₀,T ₁], if a certain controllability condition is satisfied.     

Minimax estimation of a multivariate normal mean under polynomial loss

Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix

. The problem of improving upon the usual estimator of θ, δ⁰(X) = X, is considered. An approach is developed which can lead to improved estimators, δ, for loss functions which are polynomials in the coordinates of (δ ? θ). As an example of this approach, the loss L(δ, θ) = |δ ? θ|⁴ is considered, and estimators are developed which are significantly better than δ⁰. When

is the identity matrix, these estimators are of the form $\text{δ(X) = (1 ? (}\text{b}\text{(d + |X|}{}^2\text{)}\text{))X}$.     

一类求解极值问题的ε-算法

针对极值函数的特性 ,给出了一种计算极大值函数的ε 次梯度的数值方法 ,从而构造出了一种求解极小极大问题的ε 算法 ,并且证明了算法的收敛性 ,初步的数值例子表明算法是有效的     

A new higher-order theory to laminated plates and shells

In this paper a new higher-order theory to laminated plates and shells is presented and then Symmetric and antisymmetric cross-ply laminated plates, cylindrie bending and bending of spherical shells are also studied. In order to examine the accuracy of the theory, several particular examples have been calculated. The numerical results are in good agreement with the exact solution, which shows the theory is possessed of higher accuracy and is easy to solve a problem with few unknowns.     

Topologically finite intersection property and minimax theorems

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A Chebyshev polynomial method for line integrals with singularities

In this paper we consider a Chebyshev polynomial method for the calculation of line integrals along curves with Cauchy principal value or Hadamard finite part singularities. The major point we address is how to reconstruct the value of the integral when the parametrization of the curve is unknown and only empirical data are available at some discrete set of nodes. We replace the curve by a near‐minimax parametric polynomial approximation, and express the integrand by means of a sum of Chebyshev polynomials. We make use of a mapping property of the Hadamard finite part operator to calculate the value of the integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

Superlinear elliptic boundary value problems

Summary We use a new form of the mountain pass lemma to extend results on superlinear boundary value problems. Research supported in part by an NSF grant This article was processed by the author using the LATEX style filecljour1m from Springer-Verlag.     

ON A THEOREM OF BERNSTEIN AND ITS APPLICATIONS TO WEIGHTED MINIMAX SERIES

1.IntroductionLetfbeacontinuousfunctionon[a,b].L[.willdesignatethesetofallpolynomialsofdegreelessorequalthannand11thesetofallpolyflomials.Asiswellknown,foreachntheminimaxoffisgivenby:wherepnisthebestuniformapproximationoffin11..LetusalsoconsidertileminimaxseriesgivenbytheexpressionThesetoffunctionsforwhichS*(f)=ZEd(f)相似文献   

多目标minimax问题的极大熵逼近收敛性

本文利用极大熵逼近函数，展开了多目标ｍｉｎｉｍａｘ问题的逼近方法的研究，并讨论了该逼近方法的收敛性，所得结果是目前已有的结果进一步拓广．