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.     

Least squares estimation of varying‐coefficient hazard regression with application to breast cancer dose‐intensity data

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

一基于SEM的经济发展与社会发展关系——以济南市为例

利用济南市2001—2013年的数据,构建济南市经济与社会发展关系的结构方程模型(SEM),考量经济发展的4个潜变量(经济水平、经济结构、经济增速、经济物耗)与社会发展的4个潜变量(居民的生活质量、社会稳定、人口素质、生态环境)间的相互影响,结果表明,居民生活质量正相关于人口素质和经济水平,人口素质正相关于经济水平;居民生活质量作用于社会稳定,而社会稳定是生活质量的固有要求;生态环境负相关于经济增速和经济物耗。