Anticipated Backward Stochastic Differential Equation with Reflection

In this article, we deal with anticipated backward stochastic differential equation with reflecting boundary. The existence and uniqueness of solution is obtained for equation with Lipschitz and non-Lipschitz generator.     

基于结构方程模型的农民工可雇佣性的决定因素研究——基于中部六省的调查

农民工是中国人力资源的重要组成部分。从智能、技能、体能和心能四个维度构建农民工可雇佣性模型,根据调查问卷收集数据,运用结构方程验证了农民工可雇佣性模型的合理性,研究了农民工可雇佣性及其各维度间的关系。结果表明,各维度对农民工可雇佣性影响程度依次为:技能、心能、智能和体能。农民工因年龄、文化程度不同,在可雇佣能力、技能、心能和智能方面存在显著性差异,但是在体能上没有显著差异。     

Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation

In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of ‘subsamples’ from the assumed data-generating model as well as a so-called ‘early-rejection’ strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.     

Semi-empirical likelihood inference for the ROC curve with missing data

The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performance of two or more laboratory or diagnostic tests. In this paper, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric and the other one is non-parametric and both have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It is shown that the log-semi-empirical likelihood ratio statistic is asymptotically scaled chi-squared. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. We conduct extensive simulation studies to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing probabilities.     

Dividend barrier and ruin problems for a risk model with delayed claims

In this paper, a compound Poisson risk model in the presence of a constant dividend barrier is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and and the time of delay for the claim is assumed to be random. A system of integro-differential equations with certain boundary conditions for the expected discounted penalty function is derived. We show that its solution can be expressed as the solution to the expected discounted penalty function in the same risk model with the absence of a barrier plus a linear combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Using systems of integro-differential equations for the moment-generating function as well as for the arbitrary moments of the sum of discounted dividend payments until ruin, a matrix version of the dividends–penalty type relationship is derived. We also prove that ruin is certain under constant dividend barrier strategy. The closed form expressions are given when the claim amounts from both classes are exponentially distributed. Finally, a numerical example is presented to illustrate the solution procedure.     

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.     

服装系列设计方法之“抽象方程”论

通过长期的实践教学经验总结,将服装系列设计方法与数学方程联系在一起,形成服装系列设计的"抽象方程"理论,使服装系列设计具有了定向、定量、明确、有序的特征,力求寻找一条由简到繁、由易到难、循序渐进的学习实践方法,帮助服装设计初学者尽早摆脱设计瓶颈,步入设计正轨。     

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.     

Did small and medium enterprises maintain better jobs during the early years of the recession? Job quality multidimensional evidence from Spain

While the literature has indeed confirmed a general tendency linking small and medium enterprises (SMEs) to a dynamic of greater job creation, there is little available evidence on what has happened to job quality since the financial crisis. Through a representative sample of 5311 employees in 2008 (first year of job destruction) and 4925 employees in 2010 (last year for which data were available), and using a two-stage structural equation model, this article empirically analyses the multidimensional determinants of job quality, by enterprise-size class, in Spain. The research has revealed three main results. First, job quality in Spain improved in all enterprises, regardless of their size, during the early years of the recession. Second, the greatest improvements were found in SMEs. Although job quality was already better in SMEs than in large enterprises in 2008, the differences between them subsequently widened. Third, this accelerated divergence was explained by the following dimensions: working conditions, work intensity, health and safety at work, and work–life balance. These dimensions were much more positive in SMEs. Employment-related public policy should therefore focus more specifically on SMEs. There are two reasons for this. First, despite the recession, SMEs have shown themselves to be key factors in the explanation of job quality. Second, by making changes to their value generation model, they could continue to drive the creation of better quality jobs.