估计总体方差时样本容量的选取

通过样本方差对总体方差估计时产生的误差分析，得出估计总体方差时样本容量的选取方法。     

基于平衡样本的校准估计研究--以规模以下工业企业测算为例

为解决规模以下工业企业调查中存在的样本代表性不足的问题,提出基于平衡样本的校准估计方法,并得出相应的估计量和估计量方差。该方法在抽样设计阶段采用了平衡抽样设计,在估计阶段采用了校准估计方法,较大限度地使用了辅助信息;通过数据分析得出基于平衡样本的校准估计方法要优于基于平衡抽样的HT估计方法。同时,为满足平衡变量间线性无关的假定,提出使用主成分分析、切片逆回归和切片平均方差估计三种方法对相关的平衡变量进行处理的思路。该方法对我国规模以下工业企业调查的完善具有理论与实践的双重意义,可适当的推广至我国政府统计的其他调查中。     

概率与统计的知识理解之方差

方差是描述数据集中趋势的重要指标,是进行统计决策的关键要素.通过对方差知识的深入梳理,分析样本方差分母为n和n-1的两种不同适用情形,并对在用样本估计总体统计思想下样本方差分母的校正从两个维度进行阐述与证明,有助于加强人们对方差知识的理解,做出正确的统计决策.     

对于部分线性模型的乘积调整半参估计

本文使用一种带有乘积调整的半参方法估计部分线性模型的非参数部分并给出所得估计的渐近性质。与传统的非参估计方法相比,我们所使用的半参数方法能够有效的降低所得估计的偏差,而方差不受影响。因此在积分均方误差(MISE)的意义下,该半参数方法要优于传统的估计方法。数值模拟也表明了这一点.     

混合样本方差的优良性

常见的教科书中通常采用混合样本方差作为方差相等的两个正态总体方差的估计,而对其优良性却鲜有解释.在本文中,我们证明了混合样本方差是总体方差的UMVUE,即一致最小方差无偏估计.     

强混合样本且含附加信息情形M估计和分位数估计的渐近性质（英文）

在强混合样本且含附加信息情形,本文采用经验似然方法提出了一类新的M估计和新的分位数估计.结果表明,本文提出的M估计和分位数估计具有相合性和渐近正态性,且其渐近方差比一般M估计和分位数估计的渐近方差小.     

基于部分充分降维方法的半参数多指标模型异方差检验

异方差检验是回归分析中的一类重要问题.本文针对半参数多指标模型提出具备模型自适应性的异方差检验统计量.本文所研究的半参数模型包括两类自变量,分别为主要兴趣变量X和次级兴趣变量W.一般情形下,自变量X的维数较高,经常导致非参数估计的准确性大大降低.而次级变量W的存在使得传统的充分降维方法不再适用.本文基于部分充分降维方法,构建具有维数约简特性的检验统计量,有效避免了中高维数变量带来的估计难题,同时该统计量能够自适应于潜在的真实模型结构,具备良好的稳健性.本文在理论上研究所提出的检验统计量在原假设和备择假设下的渐近性质,并通过模拟研究和实证案例分析检验方法在有限样本下的表现.     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

纵向数据半参数回归模型的最小二乘局部线性估计

本文考虑纵向数据半参数回归模型:Yij=XiTjβ+g(Tij)+iεj,基于最小二乘法和局部线性拟合的方法建立了模型中参数分量β,回归函数g(.)和误差方差σ2的估计,在适当条件下给出了估计量的相合性,通过模拟研究说明了该方法在有限样本情况下具有良好的性质。     

多源数据融合视角下非概率样本与概率样本的大量插补推断方法

随着社会的发展,概率样本无回答率越来越高,其目标变量可能存在缺失的情况.同时,大数据与网络调查的发展使得获得的样本大多数是非概率样本,如何结合这两种样本推断总体是当今时代多源数据融合领域的一个热点问题.假设存在目标变量完全缺失的概率样本和数据完整的非概率样本,提出基于非概率样本建立超总体局部多项式模型,插补概率样本缺失的目标变量,并利用插补后的概率样本估计总体,进一步证明提出估计的渐近性质.模拟和实证研究表明:与基于非概率样本的倾向得分逆加权估计相比,提出估计的绝对相对偏差,方差与均方误差更小,且与基于真实概率样本的总体估计相接近;提出总体均值估计的方差估计的绝对相对偏差与95%置信区间覆盖率也接近于基于真实概率样本的总体估计的相应指标,估计效果较好.     

随机缺失数据下样本分位数估计

分位数的估计在生物医学、社会经济调查等领域有着广泛的应用,然而在实际问题的研究中,往往由于各种人为或不可控因素造成数据收集不完全.本文在随机缺失(MAR)假设条件下,利用非参数核补法和局部多重插补法给出了响应变量缺失时样本分位数的估计,并利用经验过程等理论证明了由这两种方法得到的分位数估计的大样本性质,同时,使用重抽样方法给出了估计的渐近方差的估计,模拟结果验证了这两种方法的有效性.文章所提两种方法的优点在于:首先,所提出的缺失修正方法不需要对缺失概率的模型做任何假设;其次,方法亦适用于其他有关参数不可微的估计目标函数;最后,方法很容易地推广到一般M估计的情况,并可以对多个分位数同时进行估计.     

Confidence bands in nonparametric regression with length biased data

In this paper we deduce a confidence bands construction for the nonparametric estimation of a regression curve from length biased data, where a result from Bickel and Rosenblatt (1973,The Annals of Statistics,1, 1071–1095) is adapted to this new situation. The construction also involves the estimation of the variance of the local linear estimator of the regression, where we use a finite sample modification in order to improve the performance of these confidence bands in the case of finite samples.     

高频金融数据中市场微观结构噪音误差估计

由于在波动率估计中高频数据的使用,市场微观结构噪音的干扰对无偏的和一致的估计波动率已经变成了一种障碍,为了更好地估计真实波动率,噪音方差估计显得日益重要,本文基于目前关于波动率估计研究成果,提出了在不同的假设情况下估计市场微观结构噪音误差的方法,并与常用的估计方法进行深入的比较,得到它们的渐近性质,并且进行广泛的模拟研究它们的有限样本性质,并得到较有意义的结果。     

线性相关模型中误差方差的经验似然估计及其Bootstrap

该文利用经验似然方法，对线性相关模型中误差方差的传统最小二乘型估计进行修正，得到的修正估计其渐近方差比传统估计的更小．同时，我们还讨论了修正估计的Bootstrap逼近问题．关键词##4相关模型;;误差方差;;最小二乘;;经验似然;;Bootstrap．     

Random weighting method for Cox’s proportional hazards model

Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals.     

A Level-Value Estimation Method and Stochastic Implementation for Global Optimization

In this paper, we propose a new method, namely the level-value estimation method, for finding global minimizer of continuous optimization problem. For this purpose, we define the variance function and the mean deviation function, both depend on a level value of the objective function to be minimized. These functions have some good properties when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation equals the global minimal value of the corresponding optimization problem. We also propose an implementable algorithm of the level-value estimation method where importance sampling is used to calculate integrals of the variance function and the mean deviation function. The main idea of the cross-entropy method is used to update the parameters of sample distribution at each iteration. The implementable level-value estimation method has been verified to satisfy the convergent conditions of the inexact Newton method for solving a single variable nonlinear equation. Thus, convergence is guaranteed. The numerical results indicate that the proposed method is applicable and efficient in solving global optimization problems.     

A new method for the estimation of variance components directly from the sample covariance matrix

Statistical techniques for the estimation of variance components are usually associated with methodological and computational difficulties. In this paper a new computational method for the estimation of variance components directly from the sample covariance matrix is proposed. A comparison between this method and the maximum likelihood method for variance component estimation, based on their computational performance, is made. Cases for balanced and unbalanced simulated data assuming a two-way nixed model with correlated errors are considered, and a real-life application in animal breeding is presented.     

Option Replication in Discrete Time with Illiquidity

Abstract

This article studies a replication of a contingent claim in an illiquid market. We represent the liquidity as a supply curve in a discrete time model. Because the trade price of the illiquid asset is a function of the trade size in this model, it is important whether the contingent claim is physically settled or settled in cash. In both cases, we give a condition where a replication strategy exists uniquely and show some properties of the replication strategy. Further we analyse the liquidity cost numerically.