New Tests of Spatial Segregation Based on Nearest Neighbour Contingency Tables

Abstract.  The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause segregation or association, which are two major types of spatial patterns between the classes. These patterns can be studied using a nearest neighbour contingency table (NNCT) which is constructed using the frequencies of nearest neighbour types. Three new multivariate clustering tests are proposed based on NNCTs using the appropriate sampling distribution of the cell counts in a NNCT. The null patterns considered are random labelling (RL) and complete spatial randomness (CSR) of points from two or more classes. The finite sample performance of these tests are compared with other tests in terms of empirical size and power. It is demonstrated that the newly proposed NNCT tests perform relatively well compared with their competitors and the tests are illustrated using two example data sets.     

Model-based classification using latent Gaussian mixture models

A novel model-based classification technique is introduced based on parsimonious Gaussian mixture models (PGMMs). PGMMs, which were introduced recently as a model-based clustering technique, arise from a generalization of the mixtures of factor analyzers model and are based on a latent Gaussian mixture model. In this paper, this mixture modelling structure is used for model-based classification and the particular area of application is food authenticity. Model-based classification is performed by jointly modelling data with known and unknown group memberships within a likelihood framework and then estimating parameters, including the unknown group memberships, within an alternating expectation-conditional maximization framework. Model selection is carried out using the Bayesian information criteria and the quality of the maximum a posteriori classifications is summarized using the misclassification rate and the adjusted Rand index. This new model-based classification technique gives excellent classification performance when applied to real food authenticity data on the chemical properties of olive oils from nine areas of Italy.     

A profile likelihood method for normal mixture with unequal variance

It is well known that the normal mixture with unequal variance has unbounded likelihood and thus the corresponding global maximum likelihood estimator (MLE) is undefined. One of the commonly used solutions is to put a constraint on the parameter space so that the likelihood is bounded and then one can run the EM algorithm on this constrained parameter space to find the constrained global MLE. However, choosing the constraint parameter is a difficult issue and in many cases different choices may give different constrained global MLE. In this article, we propose a profile log likelihood method and a graphical way to find the maximum interior mode. Based on our proposed method, we can also see how the constraint parameter, used in the constrained EM algorithm, affects the constrained global MLE. Using two simulation examples and a real data application, we demonstrate the success of our new method in solving the unboundness of the mixture likelihood and locating the maximum interior mode.     

电动汽车物流配送系统的换电站选址与路径优化问题研究

在能源、环境形势日益严重的今天,电动汽车因其清洁、节能的显著优势,已经逐步成为物流配送公司重要的新能源交通工具,优化物流配送网络成为电动汽车作为物流工具普及的一个重要问题。本文提出了电动汽车物流配送系统的换电站选址与配送路径优化问题,建立了整数规划模型,并设计禁忌搜索-改进Clarke-Wright 节省的两阶段启发式算法来求解该模型,提出了两种不同的禁忌准则,并且通过算例对这两种准则进行了比较。为了证明算法的有效性,还将该算法的结果同CPLEX的计算结果进行了比较,结果表明该算法更加有效和可靠。最后,对车辆的装载容量、电池续航里程和单位建站成本做敏感性分析,发现总成本随着装载容量的增加而显著降低,电池续航里程的提升有助于降低建站成本并降低目标函数值,而单位建站成本的增加可能减少建站个数,增加运输成本,但由于续航里程的限制,建站个数也可能保持不变。     

竞争环境下的轴-辐式集装箱海运网络设计问题

针对航运企业的重组与全球扩张引起的竞争问题,提出了竞争环境下的轴-辐式集装箱海运网络设计模型。模型采用基于路径的变量作为决策变量,利用离散函数来表示航运企业与航运联盟的竞争可吸引的流量(或客户),目的在于通过设计混合轴-辐式集装箱海运网络,实现以更低的服务成本和更短的服务时间最大化可吸引的流量,建立了枢纽港口数量约束、航线连接约束、航线中转约束、流量竞争约束等,运用多点交叉遗传算法进行求解,最后结合亚欧航线的集装箱海运市场进行实例分析,对考虑客户需求多样性与航运联盟对策下的轴-辐式集装箱海运网络进行设计,并验证了算法的计算效果。     

基于核主成分分析的生态评价模型及其应用研究

利用"驱动力-压力-状态-影响-响应(DPSIR)"框架构建了生态评价指标体系。建立了基于核主成分分析的生态评价模型,并对中国10个副省级城市的生态状况进行了分析。创新与特色一是将人的需求、经济发展和社会进步等要素纳入DPSIR概念框架构建指标体系,克服了现有生态评价片面关注环境与资源状况或只关注环境保护与治理状况的不足。二是通过比较各备选核函数对应的核矩阵与最优核矩阵的相似度确定了最优核函数和最优核参数,改变了现有研究的核函数和核参数随意选取的问题。三是通过对评价指标和评价系数进行属性聚类确定影响生态评价的关键因素,改变了核主成分分析无法判断关键影响因素的问题。四是研究结果表明,影响中国副省级城市生态状况最重要的指标分别是人均绿色GDP、人均绿地面积、空气质量和万元GDP SO2排放强度;而人均居民生活用电量、人口密度和人口自然增长率对其影响很小;影响中国副省级城市生态状况的最重要的评价准则依次是驱动力、状态、压力和响应。     

Estimation and comparison of lognormal parameters in the presence of censored data

It is assumed that k(k?>?2) independent samples of sizes n _i (i?=?1, …, k) are available from k lognormal distributions. Four hypothesis cases (H ₁ – H ₄) are defined. Under H ₁, all k median parameters as well as all k skewness parameters are equal; under H ₂, all k skewness parameters are equal but not all k median parameters are equal; under H ₃, all k median parameters are equal but not all k skewness parameters are equal; under H ₄, neither the k median parameters nor the k skewness parameters are equal. The Expectation Maximization (EM) algorithm is used to obtain the maximum likelihood (ML) estimates of the lognormal parameters in each of these four hypothesis cases. A (2k???1) degree polynomial is solved at each step of the EM algorithm for the H ₃ case. A two-stage procedure for testing the equality of the medians either under skewness homogeneity or under skewness heterogeneity is also proposed and discussed. A simulation study was performed for the case k?=?3.     

The Monte Carlo EM method for estimating multivariate tobit latent variable models

We propose a multivariate tobit (MT) latent variable model that is defined by a confirmatory factor analysis with covariates for analysing the mixed type data, which is inherently non-negative and sometimes has a large proportion of zeros. Some useful MT models are special cases of our proposed model. To obtain maximum likelihood estimates, we use the expectation maximum algorithm with its E-step via the Gibbs sampler made feasible by Monte Carlo simulation and its M-step greatly simplified by a sequence of conditional maximization. Standard errors are evaluated by inverting a Monte Carlo approximation of the information matrix using Louis's method. The methodology is illustrated with a simulation study and a real example.     

Maximum likelihood estimation of stationary multivariate ARFIMA processes

This article considers the maximum likelihood estimation (MLE) of a class of stationary and invertible vector autoregressive fractionally integrated moving-average (VARFIMA) processes considered in Equation (26) of Luceño [A fast likelihood approximation for vector general linear processes with long series: Application to fractional differencing, Biometrika 83 (1996), pp. 603–614] or Model A of Lobato [Consistency of the averaged cross-periodogram in long memory series, J. Time Ser. Anal. 18 (1997), pp. 137–155] where each component y _{i, t} is a fractionally integrated process of order d _i , i=1, …, r. Under the conditions outlined in Assumption 1 of this article, the conditional likelihood function of this class of VARFIMA models can be efficiently and exactly calculated with a conditional likelihood Durbin–Levinson (CLDL) algorithm proposed herein. This CLDL algorithm is based on the multivariate Durbin–Levinson algorithm of Whittle [On the fitting of multivariate autoregressions and the approximate canonical factorization of a spectral density matrix, Biometrika 50 (1963), pp. 129–134] and the conditional likelihood principle of Box and Jenkins [Time Series Analysis, Forecasting, and Control, 2nd ed., Holden-Day, San Francisco, CA]. Furthermore, the conditions in the aforementioned Assumption 1 are general enough to include the model considered in Andersen et al. [Modeling and forecasting realized volatility, Econometrica 71 (2003), 579–625] for describing the behaviour of realized volatility and the model studied in Haslett and Raftery [Space–time modelling with long-memory dependence: Assessing Ireland's wind power resource, Appl. Statist. 38 (1989), pp. 1–50] for spatial data as its special cases. As the computational cost of implementing the CLDL algorithm is much lower than that of using the algorithms proposed in Sowell [Maximum likelihood estimation of fractionally integrated time series models, Working paper, Carnegie-Mellon University], we are thus able to conduct a Monte Carlo experiment to investigate the finite sample performance of the CLDL algorithm for the 3-dimensional VARFIMA processes with the sample size of 400. The simulation results are very satisfactory and reveal the great potentials of using the CLDL method for empirical applications.