竞争环境下基于服务约束的轴-辐式海运网络优化研究

针对同一海运市场中不同的海运企业——领导者与跟随者在设计多分配的轴-辐式海运网络时引起的竞争问题,突破已往枢纽港口集合是给定的假设,将航线连接设计扩展为可存在多条,引入基于服务约束（服务质量\价格\时间）的吸引力模型来定量表示托运人的选择行为,建立了竞争环境下基于服务约束的轴-辐式海运网络优化问题的数学模型,利用NCP函数、凝聚函数和增广Lagrange乘子罚函数法对这一问题进行求解。算例仿真结果显示：（1）跟随者在托运人考虑单位服务价格时,即使不存在规模经济效应,跟随者也可通过建立合适的枢纽港口来获取一定的市场机会;（2）跟随者在存在较大规模经济效应时其利润最可观,因采用比例模型,在不存在规模经济效应下跟随者在领导者决定设计不同数量的枢纽港口时其利润不会统一收敛于某一定值;（3）跟随者在领导者仅设计1个枢纽港口时可通过建立大量的枢纽港口来争夺丰厚的利润,但对于港口集合 N={1,2,…,12} 的海运市场,领导者只需设计2个以上枢纽港口时跟随者的利润空间便会受到较大挤压。     

Properties of Lagrangian distributions

Abstract

Lagrange’s expansion is the power series expansion of the inverse function of an analytic function, and it leads to general Lagrangian distributions of the first kind as well as of the second kind. We present some theorems in which different sets of two analytic functions provide a Lagrangian distribution. Potential applicability of the theorem to tandem queueing process is studied.     

A powerful and interpretable alternative to the Jarque–Bera test of normality based on 2nd-power skewness and kurtosis,using the Rao's score test on the APD family

We introduce the 2nd-power skewness and kurtosis, which are interesting alternatives to the classical Pearson's skewness and kurtosis, called 3rd-power skewness and 4th-power kurtosis in our terminology. We use the sample 2nd-power skewness and kurtosis to build a powerful test of normality. This test can also be derived as Rao's score test on the asymmetric power distribution, which combines the large range of exponential tail behavior provided by the exponential power distribution family with various levels of asymmetry. We find that our test statistic is asymptotically chi-squared distributed. We also propose a modified test statistic, for which we show numerically that the distribution can be approximated for finite sample sizes with very high precision by a chi-square. Similarly, we propose a directional test based on sample 2nd-power kurtosis only, for the situations where the true distribution is known to be symmetric. Our tests are very similar in spirit to the famous Jarque–Bera test, and as such are also locally optimal. They offer the same nice interpretation, with in addition the gold standard power of the regression and correlation tests. An extensive empirical power analysis is performed, which shows that our tests are among the most powerful normality tests. Our test is implemented in an R package called PoweR.     

拥堵交通网络模型和增强拉格朗日乘子算法

为了更加准确地反映拥堵网络的交通流状态,必须在传统交通网络均衡模型中添加路段容量约束条件,限制路段交通流量的非现实的增长,因此构造了一个容量制约下的均衡交通网络流模型.在拥堵交通网络中,传统的路段特征函数不能反映拥堵的交通特性,修正路段的旅行费用表示为行车时间和因为拥堵而产生的等待延迟的总和,路段容量约束条件的拉格朗日乘子等于该路段的等待延迟.把外惩罚函数和牛顿法相结合构筑成增强拉格朗日乘子算法,用来求解拥堵网络的交通流状态.外惩罚函数通过调整惩罚参数,把容量约束下的网络均衡问题转化成传统网络均衡问题.牛顿法通过移动方向、修正矩阵和移动步长的组合来保证路径或路段交通流量解的可行性,同时获得转化后子问题的最优解.     

The shapes of things to come: probability density quantiles

For every discrete or continuous location-scale family having a square-integrable density, there is a unique continuous probability distribution on the unit interval that is determined by the density-quantile composition introduced by Parzen in 1979. These probability density quantiles (pdQs) only differ in shape, and can be usefully compared with the Hellinger distance or Kullback–Leibler divergences. Convergent empirical estimates of these pdQs are provided, which leads to a robust global fitting procedure of shape families to data. Asymmetry can be measured in terms of distance or divergence of pdQs from the symmetric class. Further, a precise classification of shapes by tail behaviour can be defined simply in terms of pdQ boundary derivatives.     

Invariant tests based on M-estimators,estimating functions,and the generalized method of moments

We study the invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such as models which are formulated in terms of estimating functions (Godambe, 1960) or moment conditions and are estimated by generalized method of moments (GMM) procedures (Hansen, 1982), and models estimated by pseudo-likelihood (Gouriéroux, Monfort, and Trognon, 1984b,c) and M-estimation methods. The invariance properties considered include invariance to (possibly nonlinear) hypothesis reformulations and reparameterizations. The test statistics examined include Wald-type, LR-type, LM-type, score-type, and C(α)?type criteria. Extending the approach used in Dagenais and Dufour (1991), we show first that all these test statistics except the Wald-type ones are invariant to equivalent hypothesis reformulations (under usual regularity conditions), but all five of them are not generally invariant to model reparameterizations, including measurement unit changes in nonlinear models. In other words, testing two equivalent hypotheses in the context of equivalent models may lead to completely different inferences. For example, this may occur after an apparently innocuous rescaling of some model variables. Then, in view of avoiding such undesirable properties, we study restrictions that can be imposed on the objective functions used for pseudo-likelihood (or M-estimation) as well as the structure of the test criteria used with estimating functions and generalized method of moments (GMM) procedures to obtain invariant tests. In particular, we show that using linear exponential pseudo-likelihood functions allows one to obtain invariant score-type and C(α)?type test criteria, while in the context of estimating function (or GMM) procedures it is possible to modify a LR-type statistic proposed by Newey and West (1987) to obtain a test statistic that is invariant to general reparameterizations. The invariance associated with linear exponential pseudo-likelihood functions is interpreted as a strong argument for using such pseudo-likelihood functions in empirical work.     

基于Chandrasekharaiah广义线性理论的热压电力学的耦合广义变分原理

系统推导了热压电力学的变分原理。若应用传统的拉氏乘子法,由于会出现临界变分现象,不能得到本文的结果。本文指出临界变分是拉氏乘子的固有特性,半反推法是克服临界变分的有效途径之一。应用半反推法,根据Ｃｈａｎｄｒａｓｅｋｈａｒａｉａｈ关于压电材料的广义线性弹性理论,直接从控制方程及边初值条件,得到了经典意义上的一个耦合广义变分原理。本文的理论将给有限元方法、无单元方法及一些变分直接方法（如Ｒｉｔｚ法,Ｔ     

Model selection: A Lagrange optimization approach

This paper proposes an adaptive model selection criterion with a data-driven penalty term. We treat model selection as an equality constrained minimization problem and develop an adaptive model selection procedure based on the Lagrange optimization method. In contrast to Akaike's information criterion (AIC), Bayesian information criterion (BIC) and most other existing criteria, this new criterion is to minimize the model size and take a measure of lack-of-fit as an adaptive penalty. Both theoretical results and simulations illustrate the power of this criterion with respect to consistency and pointwise asymptotic loss efficiency in the parametric and nonparametric cases.     

Liu-type estimator in semiparametric regression models

In this paper, we introduced a Liu-type estimator for the vector of parameters β in a semiparametric regression model. We also obtained the semiparametric restricted Liu-type estimator for the parametric component in a semiparametric regression model. The ideas in the paper are illustrated in a real data example and in a Monte Carlo simulation study.     

The multiplier method in constrained estimation of covariance structure models

Based on the multiplier method of constrained minimization, an algorithm is developed to handle the constrained estimation problem in covariance structure analysis. In the context of a general model which has wide applicability in multivariate medical and behavioural researches, computer programs are implemented to produce the weighted least squares estimates and the maximum likelihood estimates. The multiplier method is compared with the penalty function method in terms of computer time, number of iterations and number of unconstrained minimizations. The indication is that the multiplier method is substantially better.