异方差的线性混合模型的参数估计

本文研究既含有固定效应又含有随机效应的线性混合模型,在随机效应的方差不同即异方差情况下,即考虑方差受外界因素的影响,如温度、湿度等,我们称之为协变量,在有协变量情况下对方差建立对数线性模型,运用最大似然估计讨论了固定效应的估计和随机效应的预测,并且用约束最大似然(REML)方法研究对数线性模型中参数和随机误差中参数(离差参数)的估计,并讨论估计量的性质及离差参数估计量的渐近正态性。     

半参数回归模型的异方差统计分析

在回归分析中，方差齐性的假设是一个普遍关心的问题．在参数和非参数回归模型中，关于异方差检验问题已经有很多的研究，见(【1】，【4】，【7】)．本文研究了半参数回归模型的异方差检验问题，得到了方差齐性检验的SCORE统计量，证明了该统计量的渐近x^2性质，最后给出计算机模拟和实际例子，推广和发展了Eubank和Thomas(1993)，韦博成(1995)的工作．     

半参数随机效应模型的异方差检验

在许多实际问题中,检验观察数据是否出现异方差性是一个相当感兴趣的问题.该文研究了半参数随机效应模型的异方差检验问题.基于Lin(1997)的方法,得到了检验方差成分都为零的Score检验统计量.通过随机模拟和实际数值例子,论证了方法的有效性.利用现有的统计软件,容易实现该文所提出的检验方法.     

时间序列期望和方差函数的半参数估计方法

以二阶差分序列为基础,针对相关系数平稳时间序列,给出了其期望函数与方差函数的半参数估计形式.核方法的运用使得无需假定非周期项的具体形式就能给出相应估计结果,避免了可能出现的假定错误.进一步,通过选取不同的判定函数,得到相应方差函数的估计结果,并对此类方法进行了理论上的总结.最后通过仿真实验验证了所提出方法的有效性.     

基于异方差的自回归预测模型的参数估计及其应用

从齐性方差的线性回归模型参数估计的最小二乘法出发,通过对统计资料的适当变换,利用加权最小二乘法,获得了异方差的线性自回归模型和四种异方差的非线性自回归模型的参数估计公式,并举例阐述了估计公式的应用.     

非线性异方差分层模型及其参数估计

提出了一类非线性异方差分层模型,研究了其固定效应和方差分量的极大似然估计问题.主要采用了期望条件最大化算法(Expectation Conditional Maximization Algorithm)和蒙特卡罗积分法(Monte-Carlo integration method).对于随机效应和模型误差的方差-协方差矩阵,本文既考虑了一般的非结构化形式,也考虑了诸如自回归(AR(1))和复合对称等的结构化形式.仿真模拟的结果显示本文提出的模型及参数估计方法表现良好.此外,本文还将该类模型和估计方法应用到中国官方经济数据上,得到了一些有意义的结论.     

含方程误差的异方差重复测量误差模型参数估计

对于含测量误差的重复测量数据,协变量与响应变量真值之间可能不存在完全匹配关系,即存在方程误差.且变量真值的测量误差方差可能与样本的某种特征有关,即存在异方差性.以此类数据为驱动,讨论了含方程误差的异方差重复测量误差模型的建模和估计问题,基于EM算法给出了模型参数的显式极大似然迭代估计.最后通过模拟计算和实例分析,讨论了模型和估计方法的有效性.     

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.     

异方差性的方差分析及其应用

张荣基．异方差性的方差分析及其应用本文就家猪育种试验比较中提出的问题,给出了单因素的异方差性的方差分析方法及应用实例     

一种单因子异方差模型的分析方法

本文提出了一种单因子异方差模型,导出这种异方差分析方法,并给出了模型中均值与方差的估计.通过对仿真和数字化设计模型数据进行检验,结果表明,采用此方法比传统方法更有效.     

半参数回归模型小波估计的强相合性

考虑半参数回归模型y_i~(n)=X_i~((n)T)β+g(t_i~(n))+ε_i~(n)(1■i■n),其中β∈R~d为未知参数,g(t)为[0,1】上的未知Borel函数,X_i~(n)为R~d上的随机设计,随机误差序列{ε_i~(n)}为鞅差序列,{t_i~(n))为[0,1]上的常数序列．本文用小波的方法得到β、g(t)的估计量分别为■_n、■_n(t),并证明了它们的强相合性．     

Semiparametric Estimation of the State of a Dynamical System with Small Noise

We consider the problem of estimation of the state of a perturbed dynamical system by observing the trajectory of a diffusion process with known small diffusion coefficient. The drift coefficient is supposed to be an unknown regular function. Asymptotic minimax lower bounds for the risk of any estimator of the state are derived and the notion of efficiency is introduced. The naïve estimator for this problem is proposed and its basic properties are discussed. It emerges that this estimator is asymptotically efficient.     

半参数回归模型小波估计的矩相合性

用小波方法,考虑半参数回归模型y_i=X_i~Tβ+g(t_i)+ε_i(1≤i≤n),其中β∈R~d为未知参数,g(t)为[0,1]上未知的Borel可测函数,X_i为R~d上的随机设计,随机误差{ε_i}为鞅差序列,{t_i}为[0,1]上的常数序列.得到参数及非参数的小波估计量的q-阶矩相合性.     

混合误差下半参数回归模型小波估计的强相合性

研究了一类半参数回归模型,利用最小二乘法和小波估计法给出了未知参数β和未知函数g(.)的估计.在误差序列为ψ-混合或φ-混合下得到了^β的强相合性,给出了^g(.)的一致强相合性和r阶矩相合性.     

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.     

L1-Norm Estimation and Random Weighting Method in a Semiparametric Model

In this paper, the L_1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L_1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method.     

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures.     

Adaptive Semiparametric Estimation of the Memory Parameter

In Giraitis, Robinson, and Samarov (1997), we have shown that the optimal rate for memory parameter estimators in semiparametric long memory models with degree of “local smoothness” β is n^−r(β), r(β)=β/(2β+1), and that a log-periodogram regression estimator (a modified Geweke and Porter-Hudak (1983) estimator) with maximum frequency m=m(β)n^2r(β) is rate optimal. The question which we address in this paper is what is the best obtainable rate when β is unknown, so that estimators cannot depend on β. We obtain a lower bound for the asymptotic quadratic risk of any such adaptive estimator, which turns out to be larger than the optimal nonadaptive rate n^−r(β) by a logarithmic factor. We then consider a modified log-periodogram regression estimator based on tapered data and with a data-dependent maximum frequency m=m(β), which depends on an adaptively chosen estimator β of β, and show, using methods proposed by Lepskii (1990) in another context, that this estimator attains the lower bound up to a logarithmic factor. On one hand, this means that this estimator has nearly optimal rate among all adaptive (free from β) estimators, and, on the other hand, it shows near optimality of our data-dependent choice of the rate of the maximum frequency for the modified log-periodogram regression estimator. The proofs contain results which are also of independent interest: one result shows that data tapering gives a significant improvement in asymptotic properties of covariances of discrete Fourier transforms of long memory time series, while another gives an exponential inequality for the modified log-periodogram regression estimator.     

固定设计下一类半参数回归模型估计的强相合性

In this paper, we consider the following semiparametric regression model under fixed design: yi=xi1β g(xi) ei. The estimators ofβ, g(·) andσ2 are obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.     

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The heteroscedasticity is inevitable for the panel data modeling in economics. The two-stage estimation method is a better means to study the heteroscedasticity, in which the basis is to select only one independent variable for samples grouping, it can cause the information used is incomplete. In this paper, we propose to select several variables for grouping using variable selection method, then k-mean algorithm is used to cluster, so the samples classification can be achieved and the heteroscedasticity estimation can be obtained. The results of real example analysis show that the method presented in this paper has obvious advantages in effectiveness and feasibility.