Normal distribution based pseudo ML for missing data: With applications to mean and covariance structure analysis

When missing data are either missing completely at random (MCAR) or missing at random (MAR), the maximum likelihood (ML) estimation procedure preserves many of its properties. However, in any statistical modeling, the distribution specification for the likelihood function is at best only an approximation to the real world. In particular, since the normal-distribution-based ML is typically applied to data with heterogeneous marginal skewness and kurtosis, it is necessary to know whether such a practice still generates consistent parameter estimates. When the manifest variables are linear combinations of independent random components and missing data are MAR, this paper shows that the normal-distribution-based MLE is consistent regardless of the distribution of the sample. Examples also show that the consistency of the MLE is not guaranteed for all nonnormally distributed samples. When the population follows a confirmatory factor model, and data are missing due to the magnitude of the factors, the MLE may not be consistent even when data are normally distributed. When data are missing due to the magnitude of measurement errors/uniqueness, MLEs for many of the covariance parameters related to the missing variables are still consistent. This paper also identifies and discusses the factors that affect the asymptotic biases of the MLE when data are not missing at random. In addition, the paper also shows that, under certain data models and MAR mechanism, the MLE is asymptotically normally distributed and the asymptotic covariance matrix is consistently estimated by the commonly used sandwich-type covariance matrix. The results indicate that certain formulas and/or conclusions in the existing literature may not be entirely correct.     

带有缺失数据的结构方程模型中的模型选择问题

结构方程模型在社会学、教育学、医学、市场营销学和行为学中有很广泛的应用。在这些领域中,缺失数据比较常见,很多学者提出了带有缺失数据的结构方程模型,并对此模型进行过很多研究。在这一类模型的应用中,模型选择非常重要,本文将一个基于贝叶斯准则的统计量,称为L_v测度,应用到此类模型中进行模型选择。最后,本文通过一个模拟研究及实例分析来说明L_v测度的有效性及应用,并在实例分析中给出了根据贝叶斯因子进行模型选择的结果,以此来进一步说明该测度的有效性。     

基于结构方程模型的市场细分方法应用研究

结构方程模型是当前研究顾客满意和顾客忠诚的主流方法之一,但基于结构方程对顾客满意和顾客忠诚进行市场细分方法的研究却十分缺乏.基于结构方程模型进行市场细分算法的应用研究,并对得出的细分结果进行了解释.     

Estimation for partially linear models with missing responses: the fixed design case

Suppose that we have a partially linear model Yi=x′iβ+g(ti)+εi with independent zero mean errorsεi,where{xi,ti,i=1,···,n}are non-random and observed completely and{Yi,i=1,···,n}are missing at random(MAR).Two types of estimators ofβand g(t)for fixed t are investigated:estimators based on semiparametric regression and inverse probability weighted imputations.Asymptotic normality of the estimators is established,which is used to construct normal approximation based confidence intervals onβand g(t).Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.     

商业布局与商场差异竞争的数学模型分析

在豪泰林模型的基础上研究商业合理布局与市场定位的问题.在模型中,通过引入刻画商品差异的变量与消费者对商品差异的偏好变量,分析得到:对于没有商品差异性的商场在布局上应该尽量远离,保持自己的市场份额;对集中在市中心的大型综合性商场应该采取差异竞争的策略,同时还应兼顾当地的消费水平结构.     

新产品供应链下考虑顾客体验效应的制造商渠道返利策略研究

随着体验经济的到来和新产品市场的竞争, 如何针对顾客体验进行渠道建设和品牌推广就显得尤为重要。本文针对新产品供应链的环境, 考虑顾客的体验效应及零售商对此所做的体验投入, 利用效用理论构建了线上和线下消费者的需求函数, 在此基础上分别探讨了批发价格模式和渠道返利模式制造商占优的供应链的决策行为, 分析了供应链各决策主体均衡解的特征, 并对渠道返利前后供应链节点企业的最优决策进行了比较, 最后用数值例子分析了制造商的返利点、零售商的体验投入水平、顾客的体验效应、旅行成本以及购买意愿等对供应链最优绩效的影响。     

考虑顾客退货和固定成本的联合补货与定价策略

为了吸引更多顾客,许多电子商务零售商允许顾客在一定时间内退货,导致其利润明显减少。同时,在补货时不仅产生依赖补货量的变动成本,而且会产生与补货量无关的固定成本。基于此,以最大化电子商务零售商的利润为目标,建立考虑顾客退货和固定成本的联合补货与定价模型,其中顾客的退货量与满足的需求呈正比。在一般需求情形下,部分刻画多期问题的最优策略;在特殊需求情形下,证明(s,S,p)策略对单期问题最优,并对多期问题的最优策略进行严格刻画。根据已有刻画为多期问题构造启发式策略。数值结果表明启发式策略近似最优;当初始库存水平足够高/低时,最优补货水平和定价随退货率与固定成本单调变化。关键词:联合补货与定价模型;顾客退货;固定成本;随机动态规划;最优策略     

考虑等待提示策略的呼叫中心流体近似方法

向顾客公布需等待的排队时间用以缓解系统拥挤是目前呼叫中心运营管理的重要手段之一。为了有效刻画等待提示策略下顾客行为变化对呼叫系统性能的影响,采用流体近似方法建立了呼叫排队系统模型。首先,通过排队分析构造等待提示影响下排队行为框架,包含带有心理行为变化特征的多种行为要素概率函数;其次,利用流体方法构建了考虑顾客重拨影响的连续排队模型,并求解了稳态条件下的系统性能指标;最后,通过与仿真模型的对比,验证了该流体近似方法的有效性与精确性。研究结果对于带有等待时间提示的呼叫中心运营具有重要指导作用。     

一种基于用户终端协助的承载分离机制

针对第五代移动通信网络双连接架构中承载分离算法执行时间间隔过长降低分离算法性能的问题,提出了一种基于用户终端协助的承载分离机制。通过构建用户满意度模型,实时计算用户对网络的满意度,根据终端的用户实时满意度和实际数据接收比向主基站发送终端的反馈消息。主基站根据用户的反馈消息及时调整承载分离比例和切换终端的连接模式。该机制可以与现有的承载分离算法相结合。系统仿真结果表明,相对于传统的承载分离算法,该机制能够提升10%的用户满意度;在通信系统负载较大时,能够提升10%的系统总吞吐量。     

Assessment of maximum likelihood PCA missing data imputation

Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non‐measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression‐based methods, with other state‐of‐the‐art methods. Copyright © 2016 John Wiley & Sons, Ltd.