The calibration of P-values,posterior Bayes factors and the AIC from the posterior distribution of the likelihood

The posterior distribution of the likelihood is used to interpret the evidential meaning of P-values, posterior Bayes factors and Akaike's information criterion when comparing point null hypotheses with composite alternatives. Asymptotic arguments lead to simple re-calibrations of these criteria in terms of posterior tail probabilities of the likelihood ratio. (Prior) Bayes factors cannot be calibrated in this way as they are model-specific.     

Estimation from Zero-Failure Data

When performing quantitative (or probabilistic) risk assessments, it is often the case that data for many of the potential events in question are sparse or nonexistent. Some of these events may be well-represented by the binomial probability distribution. In this paper, a model for predicting the binomial failure probability, P , from data that include no failures is examined. A review of the literature indicates that the use of this model is currently limited to risk analysis of energetic initiation in the explosives testing field. The basis for the model is discussed, and the behavior of the model relative to other models developed for the same purpose is investigated. It is found that the qualitative behavior of the model is very similar to that of the other models, and for larger values of n (the number of trials), the predicted P values varied by a factor of about eight among the five models examined. Analysis revealed that the estimator is nearly identical to the median of a Bayesian posterior distribution, derived using a uniform prior. An explanation of the application of the estimator in explosives testing is provided, and comments are offered regarding the use of the estimator versus other possible techniques.     

Inapproximability and approximability of maximal tree routing and coloring

Let G be a undirected connected graph. Given g groups each being a subset of V(G) and a number of colors, we consider how to find a subgroup of subsets such that there exists a tree interconnecting all vertices in each subset and all trees can be colored properly with given colors (no two trees sharing a common edge receive the same color); the objective is to maximize the number of subsets in the subgroup. This problem arises from the application of multicast communication in all optical networks. In this paper, we first obtain an explicit lower bound on the approximability of this problem and prove Ω(g^1−ε)-inapproximability even when G is a mesh. We then propose a simple greedy algorithm that achieves performance ratio O√|E(G)|, which matches the theoretical bounds. Supported in part by the NSF of China under Grant No. 70221001 and 60373012.     

同种商品不同月份期货组合风险评价模型研究及应用

以期货合约的每一交易日的对数涨跌率来反映市场风险,借助VaR风险价值法,运用加权核估计技术(WKDE)和指数加权滑动模型(EWMA),建立了基于期货组合中持有头寸不同且可以进行风险对冲的期货组合市场风险非线性叠加评价模型,解决了同种商品、不同月份期货组合每一交易日最大损失的确定问题,并通过实证研究验证了模型的实用性.该模型的特点一是借助WKDE法预测组合中单个合约每一交易日涨跌率最大日亏损值,充分体现了期货合约涨跌率的实际走势,使VaR估计更加精确.二是通过动态迁移相关系数矩阵的计算保证了模型的精确性.采用EWMA模型预测动态变化的方差-协方差矩阵,从实证的角度得到更精准的动态迁移相关系数矩阵.三是考虑了组合中多头和空头不同头寸之间的风险对冲,避免了实际中期货组合风险的线性相加而造成放大风险或减少风险的不准确性,从而能较好地保证了模型的预测精度及准确性.四是通过基于风险非线性叠加建立的期货组合风险评价模型解决了SPAN系统中期货组合风险的线性叠加问题,从而得到更合理的组合风险预测值.     

Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

The paper presents a general method of designing constant-factor approximation algorithms for some discrete optimization problems with assignment-type constraints. The core of the method is a simple deterministic procedure of rounding of linear relaxations (referred to as pipage rounding). With the help of the method we design approximation algorithms with better performance guarantees for some well-known problems including MAXIMUM COVERAGE, MAX CUT with given sizes of parts and some of their generalizations.     

出口二元边际、行业异质性与劳动生产率

基于行业异质性视角,文章主要考察出口二元边际对劳动生产率的影响.利用UN Comtrade数据库,采用HK指数法测度中国出口深度边际和出口广度边际,发现中国出口产品种类基本覆盖了世界全部种类的90％.进一步地,借助聚类分析方法综合多种因素区分行业劳动技能异质性,出口二元边际与劳动生产率关系的实证结果显示:总体上出口深度边际显著推动劳动生产率提高,出口广度边际对劳动生产率产生抑制作用.更为重要的是,出口深度边际对劳动生产率的促进作用仅存在于高技能行业,受限于行业产品技术含量和劳动技能水平等,低技能和中等技能行业出口深度边际出现贫困化增长现象.出口种类扩张的生产率损失超过出口溢出效应的生产率收益,出口广度边际对高中低技能行业劳动生产率具有不同程度的负向影响.     

New results on the likelihood ratio and score tests for the von Mises distribution

In this paper, we derive Bartlett and Bartlett-type corrections [G.M. Cordeiro and S.L.P. Ferrari 1991, A modified score test statistic having chi-squared distribution to order n ^?1 , Biometrika 78 (1991), pp. 573–582] to improve the likelihood ratio and Rao's score statistics for testing the mean parameter and the concentration parameter in the von Mises distribution. Simple formulae are suggested for the corrections valid for small and large values of the concentration parameter that do not depend on the modified Bessel functions and can be useful in practical applications.     

Optimal B-robust estimators for the parameters of the Burr XII distribution

The Burr XII distribution offers a flexible alternative to the distributions that play important role for modelling data in reliability, risk and process capability. However, estimating the shape parameters of the Burr XII distribution is a challenging problem. The classical estimation methods such as maximum likelihood and least squares are often used to estimate the parameters of the Burr XII distribution, but these methods are very sensitive to the outliers in the data. Thus, a robust estimation method alternative to the classical methods is needed to find robust estimators that are less sensitive to the outliers in the data. The purpose of this paper is to use the optimal B-robust estimation method [Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust statistics: the approach based on influence functions. New York: Wiley; 1986] to obtain robust estimators for the shape parameters of the Burr XII distribution. The simulation results show that the optimal B-robust estimators generally outperform the classical estimators in terms of the bias and root mean square errors when there are outliers in data.     

商誉和价格影响需求的易逝品动态定价与广告决策

研究需求受价格和商誉共同影响下易逝品动态定价与广告投资策略的联合决策问题。在初始库存确定的情形下,在某待定销售周期内,企业通过投入广告提升自身商誉从而拓宽市场,以企业利润最大化为目标,建立联合最优动态定价及广告投资策略模型。应用庞特里亚金极大值原理,求得不同系统参数下最优动态定价和广告投资策略及最优的销售周期。通过数值算例验证方法的有效性,结合参数灵敏度分析检验系统参数对最优策略的影响并给出相应管理意义。