基于一元线性回归模型异方差对加权最小二乘法的考察

作为普通最小二乘法的改进,加权最小二乘法用于存在异方差问题的线性回归模型的参数估计。文章通过对加权最小二乘估计量、加权最小二乘变换的分析,并结合实际例证研究发现,加权最小二乘法在应用中存在一些不足之处,因而当发现模型存在异方差时使用加权最小二乘法是存在风险的。     

一种异方差模型的两阶段估计

在异方差线性回归模型中,当模型误差项的协方差阵未知时,对异方差模型进行估计目前还没有比较好的方法。基于此,提出一种异方差模型的两阶段估计—基于异方差一致协方差阵估计,该方法将异方差一致协方差阵估计HC5m和广义最小二乘估计法结合起来,综合使用全部样本的信息,并对异方差模型进行估计。通过大量的蒙特卡洛数值模拟和实证分析,结果表明该方法具有一定的可行性和有效性。     

两变量异方差随机系数回归模型的最优设计

文章研究了具有异方差误差结构的两变量随机系数回归模型的最优设计,证明了当异方差误差结构满足一个充分条件时,模型在几类经典设计准则下的最优设计可以在设计域的顶点处获得.     

单向面板回归模型中异方差类型的确定性检验框架

结合White检验和Hausman检验,在一个检验框架内对单向面板回归模型中异方差的七种类型进行研究,将误差项中的个体效应和时间效应进行分离,给出异方差类型的确定性检验方法和步骤。应用中国城镇居民总消费、居住消费和收入的数据进行实证分析,证实异方差类型确定性检验方法的实用性和可行性。     

季节异方差序列的季节调整问题研究

季节调整是从经济序列中剔除季节成分的重要方法。季节异方差的存在,使经典的季节调整方法无法彻底分离出季节成分,致使季节调整失败。本文针对季节异方差问题提出用于季节调整的改进的HS模型,并定义改进的HS模型构造季节异方差检验LR统计量,通过蒙特卡洛模拟方法分析该检验的检验尺度和检验功效。最后,利用我国税收总额月度序列给出实证分析,并通过对比考察了改进的HS模型方法季节调整的有效性。     

一种多变量线性回归模型的异方差检验方法

文章在G-Q检验的基础上,给出了一种针对多变量的推广的G-Q异方差检验方法,并通过实例分析说明了推广的G-Q异方差检验方法的可行性和有效性。     

异方差G-Q检验方法的改进

围绕戈德菲尔德—匡特异方差检验方法(G-Q检验)展开相关问题的研究讨论,并对该检验方法进行改进。在对线性回归模型异方差检验的两个基本问题进行分析阐述的基础上,对G-Q检验中使用的F检验方法进行辨析讨论,并在应用中针对不同形式的数据条件进行拓展;以此研究为基础,设计基于线性回归模型拟合值排序的多元线性回归模型的G-Q检验方法,并对这一方法进行统计模拟和应用检验,以证实该方法良好的检验效果和简便的使用过程。     

基于EM算法的异方差性Markov机制转换模型的估计

文章将EM算法引入到对异方差性Markov机制转换模型未知参数的估计,并将研究结果运用到我国股票收益率数据的分析,结果表明,该方法很好地拟合了我国股票收益率的波动性特征.该方法为金融波动问题的未知参数估计提供了新的研究思路.     

基于小波Mallat算法和异方差模型的人民币汇率预测

文章首先用小波Mallat算法对RMB/JPY汇率一阶差分数据进行了分解和单支重构,并对单支重构后的近似分量和细节分量进行检验,证实存在条件异方差性;然后,对近似分量和细节分量分别建立了条件异方差模型,同时检验了近似分量序列与原始差分序列的"杠杆效应",显示出一致的结论;最后,对各模型的均值和波动率进行了预测,结果显示结合小波后的预测效果要优于传统的预测模型.     

蒙特卡罗方法下线性模型的异方差性检验方法

在已有的异方差性检验方法的基础上,运用蒙特卡罗方法,借助permutation检验思想,在不假定随机扰动项服从同一分布族的条件下,通过从大样本中提取大量的子样本,不断对线性模型进行拟合和检验,根据异方差为真的频率大小,给出了一种新的异方差检验方法。随机模拟表明本检验方法优于传统方法。     

Heteroscedastic Nonlinear Regression Models

A very general class of models for discrete data is introduced that includes log-linear, linear, and product models as special cases. Maximum likelihood equations are developed to yield a Fisher scoring algorithm for fitting the models to both complete and incomplete data. Two examples serve to underscore the usefulness of these models.     

Wavelet-Based Density Estimation in a Heteroscedastic Convolution Model

We consider a heteroscedastic convolution density model under the “ordinary smooth assumption.” We introduce a new adaptive wavelet estimator based on term-by-term hard thresholding rule. Its asymptotic properties are explored via the minimax approach under the mean integrated squared error over Besov balls. We prove that our estimator attains near optimal rates of convergence (lower bounds are determined). Simulation results are reported to support our theoretical findings.     

流程性材料参数估计问题探讨

流程性材料最大的特点是其变异性小。对于这类总体,现有的标准差估计方法由于既包含组间差异,又包含组内差异,常常会夸大其估计误差。针对此,首先通过抽样设计,得到具有分层抽样特点的样本;然后借鉴单值—移动极差控制图中标准差的估计方法,构造了这类总体的标准差估计量。这样构造的标准差估计量,由于其估计误差中仅包含组内方差平均水平,从而更符合该类总体变异性小的特点。实际应用表明,该标准差估计量能显著降低估计误差。     

Variance Estimation in Heteroscedastic Models by Undecimated Haar Transform

We propose a method in order to maximize the accuracy in the estimation of piecewise constant and piecewise smooth variance functions in a nonparametric heteroscedastic fixed design regression model. The difference-based initial estimates are obtained from the given observations. Then an estimator is constructed by using iterative regularization method with the analysis-prior undecimated three-level Haar transform as regularizer term. We notice that this method shows better results in the mean square sense over an existing adaptive estimation procedure considering all the standard test functions used in addition to the functions that we target. Some simulations and comparisons with other methods are conducted to assess the performance of the proposed method.     

Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator

The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministic trends. The standard normality of the Cauchy test is exploited to obtain a standard normal panel unit root test under cross-sectional dependence and time-varying volatility with an orthogonalization procedure. The article’s analysis of the joint N, T asymptotics of the test suggests that (1) N should be smaller than T and (2) its local power is competitive with other popular tests. To render the test applicable when N is comparable with, or larger than, T, shrinkage estimators of the involved covariance matrix are used. The finite-sample performance of the discussed procedures is found to be satisfactory.     

Efficient Estimation in Heteroscedastic Partially Linear Varying Coefficient Models

This article considers statistical inference for the heteroscedastic partially linear varying coefficient models. We construct an efficient estimator for the parametric component by applying the weighted profile least-squares approach, and show that it is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator reaches the semiparametric efficiency bound. Simulation studies are conducted to illustrate the performance of the proposed method.     

Parameter Estimation in Conditional Heteroscedastic Models

Abstract

We study asymptotics of parameter estimates in conditional heteroscedastic models. The estimators considered are those obtained by minimizing certain functionals and those obtained by solving estimation equations. We establish consistency and derive asymptotic limit laws of the estimators. Condition under which the limit law is normal is studied. Further, bootstrap for these estimators is discussed. The limiting distribution of the estimators is not necessary always normal, and we present a real data example to illustrate this.     

A Two-Stage Estimator of the Dependence Parameter for the Clayton-Oakes Model

This paper describes the properties of a two-stage estimator of the dependence parameter in the Clayton-Oakes multivariate failure time model. The parameter is estimated from a likelihood function in which the marginal hazard functions are replaced by estimates. The method extends the approach of Shih and Louis (1995) and Genest, Ghoudi and Rivest (1995) to allow the marginal hazard for failure times to follow a stratified Cox (1972) model. The method is computationally simple and under mild regularity conditions produces a consistent, asymptotically normal estimator.     

Estimation of Variance Function in Heteroscedastic Regression Models by Generalized Coiflets

A wavelet approach is presented to estimate the variance function in heteroscedastic nonparametric regression model. The initial variance estimates are obtained as squared weighted sums of neighboring observations. The initial estimator of a smooth variance function is improved by means of wavelet smoothers under the situation that the samples at the dyadic points are not available. Since the traditional wavelet system for the variance function estimation is not appropriate in this situation, we demonstrate that the choice of the wavelet system is significant to have better performance. This is accomplished by choosing a suitable wavelet system known as the generalized coiflets. We conduct extensive simulations to evaluate finite sample performance of our method. We also illustrate our method using a real dataset.     

我国商业银行效率评价及实证分析

内容提要：本文运用数据包络法对我国十二家主要商业银行04—06年的效率状况进行了定量考察,并在此基础上探讨了我国国有商业银行效率低下的原因,提出了提高我国银行业效率的途径。