SUR模型回归系数的估计

本文证明了一个关于SUR模型回归系数最小方差线性无偏估计(MVLUE)的充要条件,并利用此充要条件讨论了几类SUR模型回归系数的MVLUE估计及两步估计.在方法上避免了与分块矩阵求逆有关的运算,所得结论推广和完善了已有的一些结果.     

An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

Let G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is adjacent to a vertex in S and to a vertex in V−S. The restrained domination number of G, denoted γ_r(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is a connected graph of order n and minimum degree δ and not isomorphic to one of nine exceptional graphs, then .     

Statistical inference of minimum BD estimators and classifiers for varying-dimensional models

Stochastic modeling for large-scale datasets usually involves a varying-dimensional model space. This paper investigates the asymptotic properties, when the number of parameters grows with the available sample size, of the minimum- estimators and classifiers under a broad and important class of Bregman divergence (), which encompasses nearly all of the commonly used loss functions in the regression analysis, classification procedures and machine learning literature. Unlike the maximum likelihood estimators which require the joint likelihood of observations, the minimum-BD estimators are useful for a range of models where the joint likelihood is unavailable or incomplete. Statistical inference tools developed for the class of large dimensional minimum- estimators and related classifiers are evaluated via simulation studies, and are illustrated by analysis of a real dataset.     

A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes

For a given pair of finite point setsP andQ in some Euclidean space we consider two problems: Problem 1 of finding the minimum Euclidean norm point in the convex hull ofP and Problem 2 of finding a minimum Euclidean distance pair of points in the convex hulls ofP andQ. We propose a finite recursive algorithm for these problems. The algorithm is not based on the simplicial decomposition of convex sets and does not require to solve systems of linear equations.     

Minimax and maximin efficient designs for estimating the location-shift parameter of parallel models with dual responses

Minimax designs and maximin efficient designs for estimating the location-shift parameter of a parallel linear model with correlated dual responses over a symmetric compact design region are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations.     

Existence and uniqueness of bounded weak solution for non‐linear parabolic boundary value problem with equivalued surface

In this paper, we discuss the existence and uniqueness of bounded weak solution for non‐linear parabolic boundary value problem with equivalued surface and correct the mistake in Zhang Xu (Math. Meth. Appl. Sci. 1999; 22 : 259). The approach is based on L^∞ estimate of solution. Copyright © 2004 John Wiley & Sons, Ltd.