增算子不动点定理及其应用

本文建立了若干新的增算子不动点存在定理,作为应用,作者研究了在Banach空间中一类含间断项Volterra积分方程解的存在性,我们的结果改进和推广了诸多已知结果。     

问题:科学创新的起点

从问题的角度出发 ,提出了问题是科学创新的起点 ,并进一步阐述了问题的来源和问题的意义。只要我们善于从问题出发 ,立足于问题 ,我们的科学创新就会有一番新天地。     

区域经济增长与环境质量演进关系模型研究——基于环境库兹涅茨曲线

从社会福利最大化角度出发,通过设定物品消费偏好指数,建立两物品模型,推导出了区域环境最佳投资水平;在此基础上,从理论上证明了环境库兹涅茨曲线存在的依据以及在环境质量最低点和环境质量发生根本性好转的转折点的社会总投资水平。最后,得出环境质量演化过程曲线取决于社会经济发展状况,它与非环境物品生产函数和排污生产函数的技术参数、居民收入水平以及对环境物品和非环境物品的消费偏好以及国民收入分配政策等有关,而非仅仅与经济增长状况有关。     

Dynamic reliability models with conditional proportional hazards

A dynamic approach to the stochastic modelling of reliability systems is further explored. This modelling approach is particularly appropriate for load-sharing, software reliability, and multivariate failure-time models, where component failure characteristics are affected by their degree of use, amount of load, or extent of stresses experienced. This approach incorporates the intuitive notion that when a set of components in a coherent system fail at a certain time, there is a jump from one structure function to another which governs the residual lifetimes of the remaining functioning components, and since the component lifetimes are intrinsically affected by the structure function which they constitute, then at such a failure time there should also be a jump in the stochastic structure of the lifetimes of the remaining components. For such dynamically-modelled systems, the stochastic characteristics of their jump times are studied. These properties of the jump times allow us to obtain the properties of the lifetime of the system. In particular, for a Markov dynamic model, specific expressions for the exact distribution functions of the jump times are obtained for a general coherent system, a parallel system, and a series-parallel system. We derive a new family of distribution functions which describes the distributions of the jump times for a dynamically-modelled system.     

Bias correction for parameter estimates of spatial point process models

When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

The precision of regression-type estimator for incremental cost–effectiveness ratio

The estimation of incremental cost–effectiveness ratio (ICER) has received increasing attention recently. It is expressed in terms of the ratio of the change in costs of a therapeutic intervention to the change in the effects of the intervention. Despite the intuitive interpretation of ICER as an additional cost per additional benefit unit, it is a challenge to estimate the distribution of a ratio of two stochastically dependent distributions. A vast literature regarding the statistical methods of ICER has developed in the past two decades, but none of these methods provide an unbiased estimator. Here, to obtain the unbiased estimator of the cost–effectiveness ratio (CER), the zero intercept of the bivariate normal regression is assumed. In equal sample sizes, the Iman–Conover algorithm is applied to construct the desired variance–covariance matrix of two random bivariate samples, and the estimation then follows the same approach as CER to obtain the unbiased estimator of ICER. The bootstrapping method with the Iman–Conover algorithm is employed for unequal sample sizes. Simulation experiments are conducted to evaluate the proposed method. The regression-type estimator performs overwhelmingly better than the sample mean estimator in terms of mean squared error in all cases.     

Monte carlo estimates of the distributions of the random polygons of the voronoi tessellation with respect to a poisson process

A large-scale study, in which two million random Voronoi polygons (with respect to a homogeneous Poisson point process) were generated and mensurated, is described. The polygon characteristics recorded are number of sides (or vertices), perimeter, area and interior angles. A feature is the efficient “quantile” method of replicating Poisson-type random structures, which it is hoped may find useful application elsewhere.     

Piecewise FARIMA models for long-memory time series

We consider the problem of modelling a long-memory time series using piecewise fractional autoregressive integrated moving average processes. The number as well as the locations of structural break points (BPs) and the parameters of each regime are assumed to be unknown. A four-step procedure is proposed to find out the BPs and to estimate the parameters of each regime. Its effectiveness is shown by Monte Carlo simulations and an application to real traffic data modelling is considered.     

Testing for a change point in a sequence of exponential random variables with repeated values

Two test statistics are proposed for the change-point problem with repeated values when the data follow an exponential distribution. The properties of these two statistics have been studied and their asymptotic distributions under the alternative have been derived. The powers of the two test statistics are compared. Real-data examples are presented to illustrate the application of these tests.