阶乘幂的差分算子及其逆

与微分算子及其逆算子积分算子作比较,讨论了差分算子及其逆算子(和分).主要结果为关于乘积的k-阶差分的Leibniz公式(定理6.3)以及乘积的k-阶和分的对偶公式(定理6.4).显然,差分算子及其逆算子是阶乘幂多项式的方便工具.     

Two-Term Edgeworth Expansions for the Classes of U- and V-statistics

Much effort has been devoted to deriving Edgeworth expansions for various classes of statistics that are asymptotically normally distributed, with derivations tailored to the individual structure of each class. Expansions with smaller error rates are needed for more accurate statistical inference. Two such Edgeworth expansions are derived analytically in this paper. One is a two-term expansion for the standardized U-statistic of order m, m ? 3, with an error rate o(n^{? 1}). The other is an expansion with the same error rate for the distribution of the standardized V-statistic of the same order. In deriving the Edgeworth expansion, we made use of the close connection between the V- and U-statistics, which permits to first derive the needed expansion for the related U-statistic, then extend it to the V-statistic, taking into consideration the estimation of all difference terms between the two statistics.     

一类曲面族包络的求解问题

本文给出了单参数曲面族方程是参数α的二次式的曲面族包络面的一种简易解法.     

基于Lagrange多项式秘密共享技术研究

从Lagrange多项式的构造,系数和未知数的取值,Lagrange因子的计算方法和如何恢复常数项等问题出发,详细讨论了秘密的分发和恢复过程,通过仿真实验实现了一个(3,5)门限可视秘密共享方案,实验结果表明:该方法可使每个参与者对自己的子秘密及其他成员出示的子秘密进行验证。而不泄露子秘密信息,有效地阻止了外部攻击者对子秘密的窃取及内部参与者之间的互相欺诈,并可进一步推广到彩色空间,使其具有更广泛的实用价值和应用前景。     

关于多元多项式可约性的讨论

比较了多元多项式与一元多项式的可约性，并给出了艾森斯坦因判别准则在多元情形的推广．     

An efficient experiment to study superconducting ceramics

Materials formulation and processing research are important industrial processes and most materials know-how comes from physical experiments. Our impression, based on discussions with materials scientists, is that statistically planned experiments are infrequently used in materials research. This scientific and engineering area provides an excellent opportunity for both using the available techniques of statistically planned experiments, including mixture experiments, and identifying opportunities for collaborative research leading to further advances in statistical methods for scientists and engineers. This paper describes an application of SchefK's (1958) simplex approach for mixture experiments to formulation of high-temperature superconducting compounds. This example has given us better appreciation of the needs of materials scientists and has provided us opportunities for further collaborative research.     

Some as-optimal designs and their a-efficiencies

For polynomial regression over spherical regions, the d-th order As-optimal designs for γ-th order models are derived for 4 ≥ d > γ≥l. Efficiencies of these designs with respect to the γ-th order A-optimal designs are obtained. Furthermore, the effects of estimating intermediate m-th order models on these efficiencies are examined for d > m > γ     

An Appreciation of Balanced Loss Functions Via Regret Loss

We examine balanced loss functions, which account for both estimation error and goodness of fit (or proximity to a “target” estimator), in terms of their regret losses, providing new insight and interpretations. This also shows a connection between quadratic balanced loss and usual quadratic loss, which easily converts frequentist and Bayesian results for quadratic loss to related results for quadratic balanced loss and vice versa. Some implications of these results for Stein-rule estimators under linear regression are discussed. We also examine regret losses corresponding to several non-quadratic balanced loss functions.     

The coefficient of determination and its adjusted version in linear regression models

This article presents a comparative study of the efficiency properties of the coefficient of determination and its adjusted version in linear regression models when disturbances are not necessarily normal.     

On some DS-optimal designs in spherical regions

For polynomial regression over spherical regions the d-th order D_s-optimal designs for the λ-th order models are derived for 1 ≤ λ ≤ d ≤ 4. Efficiencies of these designs with respect to the λ-th order D-optimal designs are obtained. The effects of estimating addtional parameters due to an m-th order model (d ≥ m >>λ) on the efficiencies are investigated.