Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.     

义和团的三大革命口号及其历史定位

通过对义和团运动中“反清复明”——“扶清灭洋”——“扫清灭洋”三大革命口号的具体分析,阐明义和团战士的三次历史行为并确立其在中国农民革命斗争史上的历史地位,为进一步认清义和团反帝爱国的斗争性质及其伟大历史作用提供一个比较新颖的视角空间。     

绵阳出口加工区的优劣势及对策

绵阳出口加工区在优惠政策、政府扶持等方面拥有发展优势,其健康发展在提升地方城市功能、扩大就业、拉动周边地区产业发展等方面将起显著作用;但该加工区的包括区位等比较劣势也很明显,如没有得到很好解决,将直接影响其发展潜力。因此,加工区应在基础建设、招商引资和政府管理等方面加强建设。     

湖北自贸试验区的制度创新:实践特征、理论内涵与政策启示

建设湖北自贸试验区是新发展阶段全面深化改革、扩大开放的系统性探索和战略实践,从动态演进论与制度变迁、制度经济学的交易成本论以及公共经济学的公共物品供需视角,对自贸试验区制度创新的理论逻辑与实践意义予以系统研究。研究发现,湖北自贸试验区围绕加快转变政府职能、深化投资领域改革、促进贸易转型升级、推动金融开放创新、创新驱动发展以及服务国家战略等方面展开了一系列制度创新实践,逐步形成由浅入深、由线下向线上线下协同发展、由共性领域向特色领域逐步延伸、从前项到末端统筹安排、借鉴与创新并举以及集中推广与自主运用相结合的改革创新发展路径。研究认为,推动湖北自贸试验区的制度创新,充分发挥其在破解地方深层次结构性发展矛盾和扩展增长赋能空间上的功能内涵,需要在顶层制度设计方面,加强与国内国际双循环新发展格局相互衔接,通过完善监管体系设计、提升行政服务效率来转变政府监管职能和健全市场监管,构建由法律法规、行政规章、规范性文件共同组成的、与国际规范兼容协调的法制框架和政策体系,统筹为国家试制度、出经验的全局性战略目标与谋求为地区经济发展注活力、添动力的局部性现实需求之间的激励导向; 在具体实施路径层面,持续优化开放平台、营商环境和加强口岸智慧功能建设,着力培育和强化大城市、大枢纽、大口岸、大平台、大产业以及一流的营商环境等,构建开放型经济新体制和多维量化评估指标体系,实现自贸试验区制度创新实践探索、经验成效审视验证、赋能社会经济发展以及长远建设规划目标的有机协调统一,助力湖北建设新时代内陆开放新高地。     

A simple,automatic and adaptive bivariate density estimator based on conditional densities

The standard approach to non-parametric bivariate density estimation is to use a kernel density estimator. Practical performance of this estimator is hindered by the fact that the estimator is not adaptive (in the sense that the level of smoothing is not sensitive to local properties of the density). In this paper a simple, automatic and adaptive bivariate density estimator is proposed based on the estimation of marginal and conditional densities. Asymptotic properties of the estimator are examined, and guidance to practical application of the method is given. Application to two examples illustrates the usefulness of the estimator as an exploratory tool, particularly in situations where the local behaviour of the density varies widely. The proposed estimator is also appropriate for use as a pilot estimate for an adaptive kernel estimate, since it is relatively inexpensive to calculate.     

On the shrinkage of local linear curve estimators

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.     

Higher-order Bayesian Approximations for Pseudo-posterior Distributions

The theory of higher-order asymptotics provides accurate approximations to posterior distributions for a scalar parameter of interest, and to the corresponding tail area, for practical use in Bayesian analysis. The aim of this article is to extend these approximations to pseudo-posterior distributions, e.g., posterior distributions based on a pseudo-likelihood function and a suitable prior, which are proved to be particularly useful when the full likelihood is analytically or computationally infeasible. In particular, from a theoretical point of view, we derive the Laplace approximation for a pseudo-posterior distribution, and for the corresponding tail area, for a scalar parameter of interest, also in the presence of nuisance parameters. From a computational point of view, starting from these higher-order approximations, we discuss the higher-order tail area (HOTA) algorithm useful to approximate marginal posterior distributions, and related quantities. Compared to standard Markov chain Monte Carlo methods, the main advantage of the HOTA algorithm is that it gives independent samples at a negligible computational cost. The relevant computations are illustrated by two examples.     

Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.     

Multilevel maximum likelihood estimation with application to covariance matrices

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.