An identity for reflexive g-inverses in the context with BLU estimators

In sampling from finite populations conditional minimax estimators are equivalent to BLU estimators. This has been shown by Gabler (1988). If the covariance matrix is singular the BLU estimator can be represented in two different ways.     

Weighted Inverse Minimum Spanning Tree Problems Under Hamming Distance

In this paper, we consider weighted inverse minimum spanning tree problems under Hamming distance. Three models are considered: unbounded case, unbounded case with forbidden edges, and general bounded case. In terms of the method for minimum-weight node cover problem on bipartite graph, we present their respective strongly polynomial algorithms.This research is supported by TRAPOYT, National Natural Science Foundation of China (10271110, 60021201)     

用直接法识别结构系统的支承刚度

本文提出了一种识别结构系统支承刚度的新方法——直接法,这种方法是建立在广义逆矩阵的理论及计算方法基础之上的。通过大量的计算机仿真计算,证明该法不失为一种计算简便、结果稳定且精度高的识别支承刚度的有效方法。直接法的实用性亦由实验得到了验证。     

改进实孔径雷达的方位分辨力

实孔径毫米波FMCW成像雷达系统中方位分辨力与距离分辨力不匹配,影响了成像质量。本文从分析“波束效应”的本质原因出发,提出了一种利用卷积反演—广义逆滤波法,对波束进行“伪压缩”是有效地提高成像雷达方位分辨力的方法。文中给出了对雷达实测数据作“伪压缩”处理的结果,可见处理后的方位分辨力提高约4倍。     

Kronecker积AB的广义逆的表示及其应用

本文给出矩阵A和B的Kronecker积的加权Moore－Penrose逆、Drazin逆和群逆的表示，并应用这些结果给出投影算子AAMN，AMNA，AdA和AgA的行列式表示，已知的关于Moore－Penrose逆和正则逆的结果，均为本文的特例．     

Weighted empirical spacings processes

We give a complete asymptotic characterization of the supremum of weighted empirical spacings processes.     

THE non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix is diagonal

This article deals with the exact non-null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix in a multinormal distribution is diagonal. The exact non-null moments as well as the exact non-null distribution are derived. The distribution is also expressed in computable form with the help of inverse Mellin transform and calculus of residues. The results obtained in this article are useful in studying the power of testing several correlation coefficients simultaneously.     

Least squares theory for possibly singular models

In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ²V of Y in the linear model Y = Xβ + e is singular by choosing the Moore-Penrose inverse (V+XX′)⁺ instead of V^-1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described.     

Inverse Polymatroidal Flow Problem

Let D = (V, A) be a directed graph, for each vertex v V, let ⁺(v) and ^– (v) denote the sets of arcs leaving and entering v, and be intersecting families on ⁺(v) and ^–(v), respectively, and and be submodular functions on intersecting pairs. A flow f : A R is feasible if

分块Z-循环矩阵的逆与Moore-Penrose逆的一个算法

本文给出了分块Z-循环矩阵的逆与Moorc-Pcnrosc逆的一个算法。