一般约束极大极小值的梯度投影算法

对一类带等式、不等式约束的极大极小值问题进行了研究,将其转化为带等式、不等式约束的非线性规划问题,并利用梯度投影算法进行求解。该算法在有限步达到最优点或产生一系列点,且其极限点是最优点。该算法减少了计算量,克服了数值实现上的困难,证明了算法的收敛性。     

Small-sample likelihood inference in extreme-value regression models

We deal with a general class of extreme-value regression models introduced by Barreto-Souza and Vasconcellos [Bias and skewness in a general extreme-value regression model, Comput. Statist. Data Anal. 55 (2011), pp. 1379–1393]. Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as χ² with a high degree of accuracy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite-sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell [The gradient statistic, Comput. Sci. Stat. 34 (2002), pp. 206–215], and the adjusted likelihood ratio test obtained in this article. Our simulations favour the latter. Applications of our results are presented.     

Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm

Abstract.  The expectation-maximization (EM) algorithm is a popular approach for obtaining maximum likelihood estimates in incomplete data problems because of its simplicity and stability (e.g. monotonic increase of likelihood). However, in many applications the stability of EM is attained at the expense of slow, linear convergence. We have developed a new class of iterative schemes, called squared iterative methods (SQUAREM), to accelerate EM, without compromising on simplicity and stability. SQUAREM generally achieves superlinear convergence in problems with a large fraction of missing information. Globally convergent schemes are easily obtained by viewing SQUAREM as a continuation of EM. SQUAREM is especially attractive in high-dimensional problems, and in problems where model-specific analytic insights are not available. SQUAREM can be readily implemented as an 'off-the-shelf' accelerator of any EM-type algorithm, as it only requires the EM parameter updating. We present four examples to demonstrate the effectiveness of SQUAREM. A general-purpose implementation (written in R) is available.     

民族间农民婚嫁行为变迁的比较研究——来自湖北432户农户家庭的调查

研究发现,湖北农户家庭人口年龄分布呈现一种典型的"M"型,这预示着在未来10-20年湖北农村会有一次人口出生的高峰期,但新的生育高峰对未来人口快速增长的冲击程度明显要较上一高峰小得多.随着时代的变迁,受教育程度的提高,农民的婚嫁行为也发生着显著变化,主要表现在:初婚嫁年龄明显反弹,婚姻倾度显著增大,通婚半径也相应加长.尽管这一结论在民族间、村落间有些差异,但总的趋势是一致的.导致农民婚嫁行为变化的根源主要来自农村教育的普及.     

On a differential equation approach to the weighted orthogonal Procrustes problem

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.     

兰州—西宁城市区域人口密度梯度变化及内在机理研究

基于SNEF的多中心区域密度函数揭示兰州—西宁城市区域的人口密度梯度变化,进而探讨人口集聚与扩散的趋势,并建立多元回归方程来解释中心城市人口密度梯度变化的内在机理。区域密度函数的估计结果显示,兰州—西宁城市区域存在的兰州市、西宁市与临夏市三个人口高密度中心表现出不同的密度梯度变化特点,也反映出不同的人口集聚与扩散趋势。兰州市与西宁市呈现出密度梯度上升,人口向中心城市集聚的趋势;而临夏市密度梯度下降,表现出人口向外扩散的趋势。通过岭回归建立回归方程的估计结果显示,密度梯度变化主要受城市规模、第二产业从业人员比例、交通可达性等因素的显著影响,第一从业人员比例、第三产业从业人员比例以及生态环境质量对于密度梯度变化的影响不显著。     

长江中游经济圈的建设——基于梯度推移过程的思考分析

长江中游经济圈是我国实现中部崛起最重要的区域之一。通过对梯度推移过程的思考分析,对长江中游的梯度发展模式做了初步探讨。旨在通过对梯度推移过程的分析来探讨长江中游经济圈建设的点轴开发研究,从而探讨长江中游经济圈的建设问题。     

Woody vegetation and canopy fragmentation along a forest-to-urban gradient

To identify patterns that can be used to predict vegetation and landscape characteristics in urban environments, we surveyed the species composition and size of woody plants, as well as the landscape structure of forest canopies, along a forest-to-urban gradient near Oxford, Ohio, USA. The gradient included six sites of increasingly urban land-use: a preserve, a recreational area, a golf course, a residential subdivision, apartment complexes, and a business district. We recorded species identity and stem diameter for all woody plants greater than 3 cm diameter at breast height (DBH) to examine the distribution of individual species as well as overall community composition. We used digitized aerial photographs to compare the spatial characteristics of the forest canopy at each site. We found predictable patterns in species diversity (Shannon index), spatial heterogeneity in species composition (mean percent dissimilarity), and all measures of patch fragmentation (canopy cover and patch number and size). There were clear differences in tree density and total basal area between forested sites and developed sites, but there was little resolution among developed sites. Species richness and average DBH showed no clear pattern, suggesting that landscaping preference largely determined these values. We present a modified version of an intermediate heterogeneity model that can be used to predict diversity patterns in urban areas. We discuss probable mechanisms that led to these patterns and the potential implications for animal communities in urban environments.     

线性规划的梯度投影算法

Ｋａｒｍａｒｋａｒ算法是解线性规划的多项式算法，但其具有数值不稳定的缺点，同时，由于它属于内点法，在算法终止时所得的点始终是一个近似最优解。文中给出的梯度投影法，可以穿过区域内部，或穿过区域的边界的相对内部，证明了该方法将在有限步终止。