Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.     

基于动态因子Copula模型的行业间系统性风险分析

国际金融市场间的相关关系以及系统性风险受到很多学者的重视，本文则以我国股市的行业指数作为研究对象进行实证研究。通过构建动态因子Copula模型，文章对行业的日收益率数据进行了动态相关性分析，并基于风险预期占比度量了我国行业之间系统性风险的溢出效应。本文分析了2006年1月4日至2016年7月1日的28个行业指数数据，基于GAS动态负荷因子的变化路径来刻画其相关关系，通过风险预期占比来研究行业间的风险溢出效应。研究表明，各个行业指数收益率之间存在较强的关联性。就单个行业来说，化工行业与其他行业关系最为不稳定。就金融与非金融行业而言，金融行业对非金融行业的影响较大且较为平稳。本文所得研究结果可以为投资者和风险管理者在进行决策时提供一定的指导。     

Likelihood ratio tests for multivariate normality

This paper presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed tests is studied against various alternatives via Monte Carlo simulations. Simulation studies show our tests compare well with other powerful tests including multivariate versions of the Shapiro–Wilk test and the Anderson–Darling test.     

Mixtures of Gaussian copula factor analyzers for clustering high dimensional data

Mixtures of factor analyzers is a useful model-based clustering method which can avoid the curse of dimensionality in high-dimensional clustering. However, this approach is sensitive to both diverse non-normalities of marginal variables and outliers, which are commonly observed in multivariate experiments. We propose mixtures of Gaussian copula factor analyzers (MGCFA) for clustering high-dimensional clustering. This model has two advantages; (1) it allows different marginal distributions to facilitate fitting flexibility of the mixture model, (2) it can avoid the curse of dimensionality by embedding the factor-analytic structure in the component-correlation matrices of the mixture distribution.An EM algorithm is developed for the fitting of MGCFA. The proposed method is free of the curse of dimensionality and allows any parametric marginal distribution which fits best to the data. It is applied to both synthetic data and a microarray gene expression data for clustering and shows its better performance over several existing methods.     

Bayesian penalized B-spline estimation approach for epidemic models

Ordinary differential equations (ODEs) are normally used to model dynamic processes in applied sciences such as biology, engineering, physics, and many other areas. In these models, the parameters are usually unknown, and thus they are often specified artificially or empirically. Alternatively, a feasible method is to estimate the parameters based on observed data. In this study, we propose a Bayesian penalized B-spline approach to estimate the parameters and initial values for ODEs used in epidemiology. We evaluated the efficiency of the proposed method based on simulations using the Markov chain Monte Carlo algorithm for the Kermack–McKendrick model. The proposed approach is also illustrated based on a real application to the transmission dynamics of hepatitis C virus in mainland China.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

A goodness of fit test for multilevel survival data

No satisfactory goodness of fit test is available for multilevel survival data which occur when survival data are clustered or hierarchical in nature. Hence the aim of this research is to develop a new goodness of fit test for multilevel survival data and to examine the properties of the newly developed test. Simulation studies were carried out to evaluate the type ? error and the power. The results showed that the type I error holds for every combination tested and that the test is powerful against the alternative hypothesis of nonproportional hazards for all combinations tested.     

Inverse gaussian accelerated test models based on cumulative damage

The failure of a system under environmental stress often can be described by an accelerated test model which incorporates the environmental variable L. Here, the failure of such a system at environmental level L is modeled as the first passage of accumulated damage to a critical threshold value. Assuming a discrete additive damage model leads to a Birnbaum–Saunders-type distribution for the failure time which can be closely approximated by an inverse Gaussian-type model. However, if a continuous damage model based on a Gaussian process is assumed, a more general family of inverse Gaussian accelerated test models is obtained. Three sets of failure data are discussed to illustrate the usefulness of this general family.     

Flexible work planning of service agents with load balancing

This work emerged from the need to better plan the daily work of 29 travelling service agents, who provide 1090 services to 412 customers in 283 sites, on daily average. A handy and flexible tool was developed and is presented herein. A major contribution of this study is an explicit consideration of the multi-dimensional nature of the problem by the inclusion of workload balancing, which may stand in conflict to cost minimisation. Further, the geographical distribution of the demand is highly irregular. Therefore, two load measures are required and balanced. This required to fitting a proper planning scheme. The planning tool has been applied successfully by the commercial service provider. Improvements in the order of 20% and more were obtained in key performance measures. Moreover, cost reductions, service improvement and load balance were obtained simultaneously: the standard deviations of the service times and working day’s duration were reduced by 18 and 58%, respectively. This enables to reduce the number of agents with no significant harm in performance. Additional practical advantages of the proposed tool are also discussed and demonstrated, for example, the ability to cope with geographical distributions and the flexibility to respond to daily variations in demand.