平衡损失下不等式约束回归系数的线性容许估计

对回归系数在不等式约束和平衡损失下讨论了其线性估计的可容许性,给出了齐次和非齐次线性估计类中可容许估计的充要条件.     

矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.     

平衡损失下约束线性回归模型中回归系数的可容许估计

本文在平衡损失函数下得到等式约束模型中回归系数在齐次(非齐次)估计类中存在可容许估计的充要条件,给出带有不完全椭球约束模型中回归系数的线性估计在一切估计类中为可容许估计的充要条件.     

增长曲线模型回归系数线性估计的可容许性

该文讨论增长曲线模型中回归系数线性估计的可容许性, 在矩阵损失(d(Y)-KBL)(d(Y)-KBL)' 下, 分别给出了回归系数的齐次与非齐次线性估计是可容许的充要条件, 推广了以往文献的相关结论.     

带约束一般生长曲线模型中可容许线性估计的特征

本文讨论带约束一般生长曲线模型中的可容许线性估计问题,对于回归系数的线性可估函数KBL的估计DYF(DYF+M),分别在齐次和非齐次线性估计类中,给出了它们是可容许估计的一些特征.     

增长曲线模型回归系数线性估计的可容许性

本文讨论增长曲线模型回归系数线性估计的可容许性，给出了常见的三种形式不同的可容许性定义．我们在较特殊的齐次（或非齐次）线性估计类中，证明了这三种容许性的一致性，并且得到了其共同的可容许估计的充要条件．     

矩阵损失下带约束的回归系数非齐次线性估计的Minimax可容许性的特征

本文在矩阵损失下给出了带约束的回归系数线性估计在非齐次线性估计类中是Minimax可容许估计的充要条件。     

二次损失下随机回归系数和参数的线性估计是可容许的充要条件

本文对于一般的随机效应线性模型(包括混合效应线性模型),在二次损失函数下给出了随机回归系数和参数的线性可估函数的齐次线性估计(线性估计)在齐次线性估计类(线性估计类)中可容许的充分必要条件.     

平衡损失下一般Gauss—Markoff模型中回归系数的非齐次线性可容许估计

提出了适用于—般Gauss-Markoff模型的平衡损失函数,并在该平衡损失下,研究了模型中回归系数的非齐次线性估计在非齐次线性估计类中的可容许性,得到了充要条件．     

不等式约束下线性模型中线性估计的可容许性

本文研究了带有不等式约束的多指标线性模型中线性估计的可容许性.利用矩阵论的相关知识,在矩阵损失下得到了齐次线性估计在齐次线性估计类中是可容许的充要条件,以及非齐次线性估计在非齐次线性估计类中是可容许的若干条件,推广了不等式约束下可容许性的相关结果.     

增长曲线模型回归系数线性估计的泛容许性

本文讨论增长曲线模型回归系数的线性估计的容许性.我们给出了回归系数线性估计的泛容许性定义,并在某些线性估计类中得到了泛容许估计的充要条件.     

Boundedness Criterion for Some Commutators of Linear Operators

The paper is to establish a boundedness criterion for some commutators of linear operators when these linear operators don't satisfy the general A_p weight estimates but satisfy some radial weight estimates.     

一般生长曲线模型中共同均值参数线性估计的泛容许性

本文研究一般生长曲线模型中共同均值参数的估计问题,给出了共同均值参数线性估计的泛容许定义,并在较特殊的齐次与非齐次线性估计类中得到了泛容许的充要条件．     

Boundedness Criterion for Some Commutators of Linear Operators

The paper is to establish a boundedness criterion for some commutators of linear operators when these linear operators don't satisfy the general A_p weight estimates but satisfy some radial weight estimates.     

Locally extra-optimal regularizing algorithms and a posteriori estimates of the accuracy for ill-posed problems with discontinuous solutions

Local a posteriori estimates of the accuracy of approximate solutions to ill-posed inverse problems with discontinuous solutions from the classes of functions of several variables with bounded variations of the Hardy or Giusti type are studied. Unlike global estimates (in the norm), local estimates of accuracy are carried out using certain linear estimation functionals (e.g., using the mean value of the solution on a given fragment of its support). The concept of a locally extra-optimal regularizing algorithm for solving ill-posed inverse problems, which has an optimal in order local a posteriori estimate, was introduced. A method for calculating local a posteriori estimates of accuracy with the use of some distinguished classes of linear functionals for the problems with discontinuous solutions is proposed. For linear inverse problems, the method is bases on solving specialized convex optimization problems. Examples of locally extra-optimal regularizing algorithms and results of numerical experiments on a posteriori estimation of the accuracy of solutions for different linear estimation functionals are presented.     

Some new Strichartz estimates for the Schrödinger equation

We deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time-dependent potential.     

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本文综述混合效应模型参数估计方面的若干新进展. 平衡混合效应方差分析模型的协方差阵具有一定结构. 对这类模型, 文献[1]提出了参数估计的一种新方法, 称为谱分解法. 新方法的突出特点是, 能同时给出固定效应和方差分量的估计, 前者是线性的, 后者是二次的,且相互独立. 而后, 文献[2--9]证明了谱分解估计的进一步的统计性质, 同时给出了协方差阵对应的估计, 它不仅是正定阵, 而且可获得它的风险函数, 这些文献还研究了谱分解估计与方差分析估计, 极大似然估计, 限制极大似然估计以及最小范数二次无偏估计的关系. 本文综述这一方向的部分研究成果, 并提出一些待进一步研究的问题.     

几类高阶线性微分方程亚纯解的增长性

本文研究了几类亚纯函数系数的高阶线性微分方程解的增长性问题,得到了齐次和非齐次线性微分方程亚纯解增长性的精确估计.     

Linear estimates of accuracy for approximate solutions of inverse problems

In this paper, we explore the question of which non-linear inverse problems, which are solved by a selected regularization method, may have so-called linear a priori accuracy estimates – that is, the accuracy of corresponding approximate solutions linearly depends on the error level of the data. In particular, we prove that if such a linear estimate exists, then the inverse problem under consideration is well posed, according to Tikhonov. For linear inverse problems, we find that the existence of linear estimates lead to, under some assumptions, the well-posedness (according to Tikhonov) on the whole space of solutions. Moreover, we consider a method for solving inverse problems with guaranteed linear estimates, called the residual method on the correctness set (RMCS). The linear a priori estimates of absolute and relative accuracy for the RMCS are presented, as well as analogous a posteriori estimates. A numerical illustration of obtaining linear a priori estimates for appropriate parametric sets of solutions using RMCS is given in comparison with Tikhonov regularization. The a posteriori estimates are calculated on these parametric sets as well.     

Sharp estimates of multilinear operators in polydisk and unit ball

Sharp estimates for some multifunctional analytic expressions and multilinear operators are given, generalizing the corresponding estimates for a single function or for a linear operator.