动态异方差随机前沿模型的Bayesian推断

随机前沿模型中如果忽略单边干扰项的异质性(heterogeneity)往往导致错误的效率估计.从个体特征的影响和方差的时变性两方面对单边干扰项进行考虑,提出异方差动态随机前沿模型.利用Gibbs抽样方法对动态异方差随机前沿模型进行Bayesian分析.导出了模型参数的后验条件分布,对中小样本的模拟实验显示在最小后验均方误差准则下得到的参数估计值非常接近真值.对电力公司的实际数据进行分析显示对数无效率项的方差有一定的时变性.     

误差绝对值的统计特征和应用

在误差服从正态分布的情况下,研究了误差绝对值的分布、数学期望和方差等统计特征,推导了高阶矩的计算公式;给出了利用残差绝对值对正态分布标准差进行估计的简便方法,残差的变异系数和分布情况可用于考察残差是否服从正态分布,利用误差限和误差平均值及正态分布标准差的关系可对模拟模型中的误差进行控制。     

线性模型误差方差的经验似然估计

本文应用经验似然方法得到了线性模型误差方差的一类新的估计,证明了估计的渐近分布为正态分布且渐近方差不超过常用的误差方差估计的渐近方差,同时给出了渐近方差的显式表达.     

线性模型误差方差的经验似然估计（英文）

本文应用经验似然方法得到了线性模型误差方差的一类新的估计,证明了估计的渐近分布为正态分布且渐近方差不超过常用的误差方差估计的渐近方差,同时给出了渐近方差的显式表达.     

具有NA误差项的多元回归模型中最小二乘估计的强相合性

在具有NA误差项的多元回归模型中,对误差项和设计矩阵作了一定的限制条件下给出了其最小二乘估计的强相合性;进而得出了NA序列的样本均值的加权和的几乎处处收敛性的结论.     

空间自相关地理加权回归模型的估计

地理加权回归作为一类能有效处理回归分析中空间非平稳性现象的建模技术,在多类问题的研究得到了广泛的应用.主要讨论这类空间计量经济学模型在空间自相关情形下的估计问题.首先,对于因变量含有空间滞后项的地理加权回归模型,分别给出了局部似然估计和两步估计两种方法.其次,考虑了误差空间自相关下地理加权回归模型的估计问题.     

双相依结构下离散时间风险模型的破产概率渐近估计及数值模拟

本文研究了具有双相依结构及重尾索赔噪声项的离散时间风险模型的有限时间破产概率.在该模型中,索赔额服从具有独立同分布噪声项的单边线性过程;保险公司的风险投资和无风险投资导致的随机折现因子与单边线性过程的噪声项相依.保险公司单期保费收入是恒定的常数,当单边线性过程的噪声项服从重尾分布时,本文得到离散时间风险模型有限时间破产概率的渐近估计.最后利用蒙特卡罗模拟方法验证所得结果.     

线性回归模型Bootstrap LM-Error检验的水平扭曲

基于OLS估计残差,本文将Bootstrap方法用于空间误差相关性LM-Error检验,综合考虑Bootstrap模拟抽样次数、空间衔接结构以及样本量,研究并比较空间误差相关Bootstrap LM-Error检验与渐近检验的水平扭曲。大量Monte Carlo实验结果显示,当模型误差不满足独立正态分布的假设条件时,空间误差相关LM-Error渐近检验的水平扭曲较大,采用Bootstrap方法可以较好地降低该水平扭曲;不管模型误差是否满足独立正态分布的假设条件,Bootstrap方法均能够有效地降低LMError渐近检验的水平扭曲。     

由Fourier系数确定的函数类的最佳m-项单边逼近渐近估计

结合最佳m项逼近和单边逼近的思想引进所谓最佳m项单边逼近的概念,给出由Fourier系数确定的光滑函数类通过三角函数系在Lp(1≤P≤∞)的最佳m-项单边逼近渐近估计以及m-项类贪婪单边逼近结果.     

一类相依索赔离散风险模型的有限时间破产概率估计

本文研究一类具有相依索赔及重尾索赔噪声项的离散风险模型有限时间破产概率.在该模型中,索赔额服从具有独立同分布噪声项的单边线性过程;由保险公司的风险投资和无风险投资导致的随机折现因子与单边线性过程的噪声项相独立;保险公司的保费率是恒定的常数.当单边线性过程的噪声项服从重尾分布时,本文得到该离散风险模型有限时间破产概率的渐近估计.     

Group Classification and Generalized Conditional Symmetry Reduction of the Nonlinear Diffusion–Convection Equation with a Nonlinear Source

The generalized conditional symmetry method, which can be considered a generalization of the conditional symmetry method, is used to study the nonlinear diffusion–convection equations with a nonlinear source. In particular, exponential and power law diffusivities are examined and we obtain mathematical forms of the convective term and the source term, which permit the generalized conditional symmetry reductions. A number of examples are considered and some exact solutions are constructed via the compatibility of the generalized conditional symmetry and the considered equation.     

具有GARCH-skew-t误差项的时序的单位根检验

本文通过随机模拟,分析条件分布为偏t分布、具有自回归条件异方差误差项的时间序列的ADF单位根检验的临界值、检验的有效性和实际显著水平的扭曲分析。结果显示,随着波动持久性的增强,已不能直接使用Fu ller的临界值表。     

Stability estimates for the solution to the problem of determining the kernel of a viscoelastic equation

For an integrodifferential equation corresponding to a two-dimensional viscoelastic problem, we study the problem of defining the spatial part of the kernel involved in the integral term of the equation. The support of the sought function is assumed to belong to a compact domain Ω. As information for solving this inverse problem, the traces of the solution to the direct Cauchy problem and its normal derivative are given for some finite time interval on the boundary of Ω. An important feature in the statement of the problem is the fact that the solution of the direct problem corresponds to the zero initial data and a force impulse in time localized on a fixed straight line disjoint with Ω. The main result of the article consists in obtaining a Lipschitz estimate for the conditional stability of the solution to the inverse problem under consideration.     

Spatial Autocorrelation for Subdivided Populations with Invariant Migration Schemes

For populations with geographic substructure and selectively neutral genetic data, the short term dynamics is a balance between migration and genetic drift. Before fixation of any allele, the system enters into a quasi equilibrium (QE) state. Hössjer and Ryman (2012) developed a general QE methodology for computing approximations of spatial autocorrelations of allele frequencies between subpopulations, subpopulation differentiation (fixation indexes) and variance effective population sizes. In this paper we treat a class of models with translationally invariant migration and use Fourier transforms for computing these quantities. We show how the QE approach is related to other methods based on conditional kinship coefficients between subpopulations under mutation-migration-drift equilibrium. We also verify that QE autocorrelations of allele frequencies are closely related to the expected value of Moran’s autocorrelation function and treat limits of continuous spatial location (isolation by distance) and an infinite lattice of subpopulations. The theory is illustrated with several examples including island models, circular and torus stepping stone models, von Mises models, hierarchical island models and Gaussian models. It is well known that the fixation index contains information about the effective number of migrants. The spatial autocorrelations are complementary and typically reveal the type of migration (local or global).     

A stability estimate for a solution to an inverse problem of electrodynamics

We consider the integrodifferential system of equations of electrodynamics which corresponds to a dispersive nonmagnetic medium. For this system we study the problem of determining the spatial part of the kernel of the integral term. This corresponds to finding the part of dielectric permittivity depending nonlinearly on the frequency of the electromagnetic wave. We assume that the support of dielectric permittivity lies in some compact domain Ω ⊂ ℝ³. In order to find it inside Ω we start with known data about the solution to the corresponding direct problem for the equations of electrodynamics on the whole boundary of Ω for some finite time interval. On assuming that the time interval is sufficiently large we estimate the conditional stability of the solution to this inverse problem.     

约束线性模型的条件部分根方估计

对于线性约束下的线性回归模型,针对设计矩阵的病态问题,提出一种条件部分根方估计.并在均方误差矩阵准则和Pitman Closeness准则下,比较了条件部分根方估计相对于约束最小二乘估计的优良性.     

源项反演问题的条件稳定性

对于一维扩散方程的源项反演问题,探讨了反问题数据的相容性并应用积分恒等式方法建立了非线性源项反演的一种稳定性.     

基于广义条件AR(p)利率下的生存年金精算现值模型及其应用

本文利用时间序列理论将投资利率为条件 AR(p)模型推广为广义条件 AR(p)模型 ,得到利息力模型的一阶矩和二阶矩 ;针对年末支付的定期生存年金 ,利用生存年金理论得到广义条件 AR(p)利率模型下生存年金的精算现值模型 ,这对保险人合理制定保费标准和规避风险等问题具有重要理论指导意义和实际应用价值 .     

Modelling of spatial variability of soil undrained shear strength by conditional random fields for slope reliability analysis

Conditional random field model can make best use of limited site investigation data to properly characterize the spatial variation of soil properties. This paper aims to propose a simplified approach for generating conditional random fields of soil undrained shear strength. A numerical method is adopted to validate the effectiveness of the proposed approach. With the proposed approach, the analytical posterior statistics of spatially varying undrained shear strength conditioned on the known values at measurement locations can be obtained. The conditional random field model of undrained shear strength is constructed using the field vane shear test data at a site of the west side highway in New York and the probability of slope failure is estimated by subset simulation. A clay slope under undrained conditions is investigated as an example to illustrate the proposed approach. The effects of borehole location and borehole layout scheme on the slope reliability are addressed. The results indicate that the proposed approach not only can well incorporate the limited site investigation data into modelling of the actual spatial variation of soil parameters by conditional random fields, but also can capture the depth-dependent nature of soil properties. The realizations of conditional random fields generated by the proposed approach can be well constrained to the site investigation data.     

The Construction of Multivariate Distributions from Markov Random Fields

We address the problem of constructing and identifying a valid joint probability density function from a set of specified conditional densities. The approach taken is based on the development of relations between the joint and the conditional densities using Markov random fields (MRFs). We give a necessary and sufficient condition on the support sets of the random variables to allow these relations to be developed. This condition, which we call the Markov random field support condition, supercedes a common assumption known generally as the positivity condition. We show how these relations may be used in reverse order to construct a valid model from specification of conditional densities alone. The constructive process and the role of conditions needed for its application are illustrated with several examples, including MRFs with multiway dependence and a spatial beta process.