协变量缺失情形下的逆概率加权众数回归估计

数据缺失在实际应用中普遍存在,数据缺失会降低研究效率,导致参数估计有偏.在协变量随机缺失(MAR)的假定下,本文基于众数回归和逆概率加权估计方法对线性模型进行参数估计.该方法结合参数Logistic回归和非参数Nadaraya-Watson估计两种倾向得分估计方法,分别构建IPWM-L估计量和IPWM-NW估计量.模拟研究和实例分析表明,众数回归模型比均值回归模型更具稳健性,逆概率加权众数(IPWM)估计方法在缺失数据下表现出了更好的拟合效果,与IPWM-L估计量相比, IPWM-NW估计量更稳健.     

非参数方法下条件矩限制回归模型的广义矩估计

本文讨论条件矩限制回归模型的参数估计.使用非参数估计方法给出条件密度和条件均值的估计,在此基础上给出参数的广义矩估计.进一步讨论了估计的渐近正态性.     

截断指数威布尔-帕累托组合模型

使用组合模型模拟单峰厚尾型保险损失数据是非常有效的方法.鉴于在非寿险合约中一般都具有免赔条款的特征,构建一类截断指数威布尔-帕累托组合模型,讨论模型的相关统计性质,然后利用R语言对仿真数据进行参数估计及模型检验.最后,使用丹麦火险数据进行分布拟合,实证结果表明,截断指数威布尔-帕累托组合模型具有更优的拟合效果.     

关于参数设计的一个注记

本文提出了参数设计中方差估计的一种新方法 -非参数估计方法 ,用以代替田口的信噪比中的方差估计。实例表明 ,该方法不但可以对因子进行分类 ,而且可以进行模型拟合的检查     

基于变量选择的混合时空地理加权回归参数估计

混合时空地理加权回归模型作为一种有效处理空间数据全局平稳和局部非平稳的分析方法得到了广泛的应用.但其参数估计方法中假定固定系数变量已知且不存在时空效应,这一较强的前提使回归系数的估计值变得极不稳定.为探究当固定系数变量存在时空效应时的参数估计方法,本文提出一种变量选择(Variable Selection)方法来剔除指标间的交互效应,并给出相应的算法过程.通过乌鲁木齐市商品住宅真实价格数据对不同估计方法进行对比验证,结果表明,利用变量选择方法后得到的MGTWR模型性能和拟合效果得到提升,固定回归系数的估计更加稳定,原有参数估计方法得到改善.     

二叉树模型的参数估计

二叉树模型是期权定价中被广泛使用的模型之一, 其参数估计对于期权定价具有重要影响. 本文给出了一种二叉树模型参数估计方法, 该方法克服了二叉树模型经典参数估计方法的缺陷, 特别地, 消除了主观概率设定对参数估计的影响.     

NA样本半参数回归模型估计的矩相合性

考虑了误差为NA序列的半参数回归模型,利用非参数估计方法给出了模型参数的最小二乘估计和加权最小二乘估计,并在适当条件下得到了它们的矩相合性.     

纵向数据下半参数回归模型的统计分析

对于纵向数据下半参数回归模型,基于广义估计方程和一般权函数方法构造了模型中参数分量和非参数分量的估计.在适当的条件下证明了参数估计量具有渐近正态性,并得到了非参数回归函数估计量的最优收敛速度.通过模拟研究说明了所提出的估计量在有限样本下的精确性.     

基于极值理论高龄死亡率模型的比较研究

基于极值理论模型,对中国与日本高龄人口死亡率进行拟合和预测,克服了其他死亡率参数外推模型的主观性.在极值理论高龄死亡率模型的基础上使用加权最小二乘法,通过反复试验方式选择最优门限年龄和模型参数估计值,并且预测中国与日本人口最高年龄以及最高年龄区间估计.此研究为我国经验生命表的编制工作提供借鉴.     

参数估计在最优化模型中的有效性及修正

证明了在涉及随机变量的最优化模型中,如果将参数估计和最优化求解过程分离,实际得到的最优化结果必然低于理论值,即参数估计在最优化模型中总是造成低效的结果。然后给出了两种可行的参数估计修正方法。     

基于半参数可加自回归模型的黄金价格实证分析

大量实证研究表明,半参数自回归模型较传统的线性回归而言,能更好的拟合实际数据。本文构造了一类半参数可加自回归模型,基于条件最小二乘方法及核估计方法给出了估计模型参数和未知函数的迭代算法,讨论了估计量的渐近性质。通过数值模拟验证了估计的效果。并将模型应用于黄金价格数据的实证分析之中。实证分析结果表明,我们对现有模型的改进是必要的。     

Statistical Inferences of Risk Premium under the Generalized Exponential Premium Theory

The principle of exponential premium is an important premium principle in non-life actuarial science. This paper proposes an improved exponential premium principle. This premium principle can not only include the principle of exponential premium as a special case, but also the generalizations of Esscher premium principle and net premium principle, which has many excellent properties as a premium principle. We study the maximal likelihood estimates, nonparametric estimates and Bayesian estimation of risk premium, and discuss the statistical properties including asymptotic unbiased, coincidence, and asymptotic normality. In addition, the asymptotic confidence interval for this risk premium is given. Finally, the convergence rate of maximum likelihood estimation and nonparametric estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample size is small.     

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??The principle of exponential premium is an important premium principle in non-life actuarial science. This paper proposes an improved exponential premium principle. This premium principle can not only include the principle of exponential premium as a special case, but also the generalizations of Esscher premium principle and net premium principle, which has many excellent properties as a premium principle. We study the maximal likelihood estimates, nonparametric estimates and Bayesian estimation of risk premium, and discuss the statistical properties including asymptotic unbiased, coincidence, and asymptotic normality. In addition, the asymptotic confidence interval for this risk premium is given. Finally, the convergence rate of maximum likelihood estimation and nonparametric estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample size is small.     

人口增长率的非参数自回归预测模型

针对传统的人口增长预测模型不能理想地捕获我国人口增长率数据的非线性性特征,本文基于局部线性非参数估计理论,对我国建国以来的年人口增长率建立了非参数自回归NAR(1)模型,并对2000-2003年的年人口增长率进行了预测,计算结果表明,相对于参数自回归模型而言,非参数自回归模型能够很好地解决人口增长预测这一非线性问题,预测精度较高。     

半变系数模型PLS估计的渐近正态性

半变系数模型在统计建模中具有重要的应用．最近几年，人们提出了许多方法来估计其常系数和函数系数，但是估计的渐近性质还没有被系统的研究．本文介绍了半变系数模型的PLS估计，在Fan和Huang对常系数渐近性质研究的基础上，给出了函数系数的渐近正态性。     

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??In the last few decades, longitudinal data was deeply research in statistics science and widely used in many field, such as finance, medical science, agriculture and so on. The characteristic of longitudinal data is that the values are independent from different samples but they are correlate from one sample. Many nonparametric estimation methods were applied into longitudinal data models with development of computer technology. Using Cholesky decomposition and Profile least squares estimation, we will propose a effective spline estimation method pointing at nonparametric model of longitudinal data with covariance matrix unknown in this paper. Finally, we point that the new proposed method is more superior than Naive spline estimation in the covariance matrix is unknown case by comparing the simulated results of one example.     

Stahel-Donoho kernel estimation for fixed design nonparametric regression models

This paper reports a robust kernel estimation for fixed design nonparametric regression models. A Stahel-Donoho kernel estimation is introduced, in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points. Based on a local approximation, a computational technique is given to approximate to the incomputable depths of the errors. As a result the new estimator is computationally efficient. The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error. Unlike the depth-weighted estimator for parametric regression models, this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one. Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.     

Bayesian Semiparametric Density Estimation and Model Verification Using a Logistic–Gaussian Process

This article proposes a semiparametric model, which consists of parametric and nonparametric components, for density estimation. The parametric component represents the researcher's a priori beliefs about a likely family of density functions. The nonparametric component, which is modeled by a logistic–Gaussian process, allows the predictive distribution to deviate from the parametric family if it is inadequate. Bayesian hypothesis testing is used to examine the adequacy of the parametric model relative to the flexible alternative provided by the semiparametric model. The article presents a Markov chain Monte Carlo algorithm that efficiently handles the large number of parameters.     

非参数理论综述

对非参数理论进行了系统地综述.非参数理论中一个比较重要的内容是估计方法,常见的非参数估计方法有核估计、局部多项式估计、近邻估计等.光滑参数的选取、"维数灾难"与边界点问题也是与非参数理论有关的重要内容,也对这些方面进行综述.最后,文章还综述了非参数技术在时间序列模型中的有关应用问题.     

Robust Depth-Weighted Wavelet for Nonparametric Regression Models

In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method.