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.     

指数分布参数基于不完全数据的区间估计

对不完全样本观测数据,讨论了指数分布总体参数的区间估计;给出了构造置信区间的一种方法并推导出了相应的分布密度函数表达式;并说明了该方法在样本中可能存在异常值时的应用。     

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.     

多重制度逻辑与产业扶贫项目的异化 ——组织场域的视角

作为扶贫开发的重要途径,产业扶贫在实践过程中常常出现瞄不准或瞄准了但效果不突出的情形,组织场域为揭示其中的奥秘提供了有益视角。Y村的案例表明,在产业扶贫的组织场域内,地方政府与烟草公司在各自领域制度环境的制约下对自身参与产业扶贫的行为作出适应性的调整,改变了产业扶贫场域内的资讯交换渠道与资源传递方式,进而形成了组织行为主体参与产业扶贫的隐形运行逻辑。循此逻辑,非正式权力与利益的勾连固化了组织行为主体的权力关系与场域位置,扶贫资源经由村委会与合作社的承接更多流向村干部及种植大户等村庄精英群体,贫困农户则处于边缘位置。组织场域内中心--边缘关系结构的形成最终导致产业扶贫实践中制度表达与项目实践的背离。     

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.     

水平井分段多簇压裂缝间干扰研究

水平井分段多簇压裂在现场得到了广泛运用，其压裂过程中普遍存在缝间干扰现象。缝间干扰有助于形成复 杂裂缝网络以提高储层导流能力，但是也会导致起裂困难，甚至形成砂堵。因此有必要对分段多簇压裂的缝间干扰问 题进行研究。对此，基于弹性力学建立了分析多簇裂缝诱导应力的数学模型，从起裂压力、裂缝宽度、簇间距等多方面 研究了缝间干扰对水平井分段多簇压裂施工的影响。模拟结果显示，诱导应力会导致起裂压力升高、裂缝变窄，严重 时将造成压裂施工失败。通过进行分析，给出了起裂过程及延伸过程中缝间干扰的影响关系。分析认为，利用缝间干 扰提高改造体积时应当控制簇间距防止对压裂施工造成负面影响。研究结论对优化水平井分段多簇压裂设计具有指 导意义。     

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.