自变量可重复观测的线性EV模型

研究了仅自变量可以做重复观测的线性EV模型, 构造了模型回归系数的估计, 并在适当条件下证明了估计量的相合性和渐近正态性. 所得结果揭示了与自变量和因变量同步重复观测模型的差异.     

有重复观测时EV模型修正极大似然估计的相合性

研究了在一些实验点有重复观测时一维线性EV模型的参数估计问题 .在适当的条件下证明了估计的强弱相合性     

EV多项式模型的估计

给出在一些试验点有重复观测时EV多项式模型系数的估计. 在一般条件下证明了估计是强相合的.     

有重复观测时二次EV模型参数的强相合性

给出了在一些实验点重复观测时二次EV模型参数的估计，在一般条件下证明了估计是强相合的。     

有重复观测的变系数EV模型的参数估计

构造了有重复观测的变系数EV模型中的诸多参数估计,包括系数函数、测量误差方差以及测量误差与回归误差的协方差等估计,去除了有关测量误差方差已知或可靠比已知的假定.在一些较弱的条件下,证明了所有的这些估计都是强相合的,同时获得了系数函数估计的渐近正态性以及收敛速度.     

有重复观测的部分线性EV模型的参数估计

构造了有重复观测的部分线性EV模型中的诸多参数估计, 包括回归系数、回归误差方差以及非参数函数估计, 去除了有关经典文献中关于测量误差方差已知的假设. 在一些正则条件下, 证明了所有这些估计都是强相合的, 同时获得了回归系数估计的渐近正态性、非参数函数估计的最优收敛速度. 模拟计算表明这些估计的效果优良.     

非时齐扩散模型中扩散系数的局部估计

基于非时齐扩散模型的离散观测样本,利用局部近似的方法,构造了扩散系数的局部估计量,并证明了估计量的强相合性和渐近正态性.     

正倒向随机微分方程的参数估计

本文的研究目标是离散观测下正倒向随机微分方程中未知参数的估计及其性质.作为第一步,本文考虑一个线性模型.本文先导出两个状态过程的关系式,进而找到离散观测数据的似然函数.最后详细讨论最大似然估计量的相合性和渐近正态性.     

回归模型为线性的一个检验法

本文在不假定有重复观察的情况下,提出了—个检验回归函数是否为线性函数的方法,证明了其相合性并考察了其渐近功效。     

局部平稳扩散模型中时变参数的加权最小二乘估计

基于离散观测样本,利用局部线性拟合,得到了局部平稳扩散模型中时变漂移参数的加权最小二乘估计,并讨论了估计量的相合性,渐近正态性和一致收敛速度.同时,通过模拟研究说明了估计量的有效性.     

Progress in the studies of “solar activity and its geo-space Effects”

Estimators are presented for the coefficients of the polynomial errors-in-variables (EV) model when replicated observations are taken at some experimental points. These estimators are shown to be strongly consistent under mild conditions.     

Orthoregressive estimates for the parameters of systems of linear difference equations

The problem of estimating the parameters of linear difference systems of equations from the observations of the segments of solutions with additive stochastic perturbations is considered. The methods of multivariate orthogonal regression are applied to obtain the estimators. The results of comparative study of the methods are exposed from the standpoint of information on linear constraints in observations. The properties of the estimators in the limit cases of a gross sample are studied. For small perturbations, a scheme for comparison of estimators by linear approximations is proposed.     

Asymptotically optimal estimation in the linear regression problem in the case of violation of some classical assumptions

We consider the problem of estimating the unknown parameters of linear regression in the case when the variances of observations depend on the unknown parameters of the model. A two-step method is suggested for constructing asymptotically linear estimators. Some general sufficient conditions for the asymptotic normality of the estimators are found, and an explicit form is established of the best asymptotically linear estimators. The behavior of the estimators is studied in detail in the case when the parameter of the regression model is one-dimensional.     

Estimation of Parameters of Partially Linear Errors-in-variables Models with Replicated Net Points of Observation

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.     

On estimation of measurement error models with replication under heavy-tailed distributions

Measurement error (errors-in-variables) models are frequently used in various scientific fields, such as engineering, medicine, chemistry, etc. In this work, we consider a new replicated structural measurement error model in which the replicated observations jointly follow scale mixtures of normal (SMN) distributions. Maximum likelihood estimates are computed via an EM type algorithm method. A closed expression is presented for the asymptotic covariance matrix of those estimators. The SMN measurement error model provides an appealing robust alternative to the usual model based on normal distributions. The results of simulation studies and a real data set analysis confirm the robustness of SMN measurement error model.     

Multiple imputation and other resampling schemes for imputing missing observations

The problem of imputing missing observations under the linear regression model is considered. It is assumed that observations are missing at random and all the observations on the auxiliary or independent variables are available. Estimates of the regression parameters based on singly and multiply imputed values are given. Jackknife as well as bootstrap estimates of the variance of the singly imputed estimator of the regression parameters are given. These estimators are shown to be consistent estimators. The asymptotic distributions of the imputed estimators are also given to obtain interval estimates of the parameters of interest. These interval estimates are then compared with the interval estimates obtained from multiple imputation. It is shown that singly imputed estimators perform at least as good as multiply imputed estimators. A new nonparametric multiply imputed estimator is proposed and shown to perform as good as a multiply imputed estimator under normality. The singly imputed estimator, however, still remains at least as good as a multiply imputed estimator.     

A class of estimators of the mean survival time from interval censored data with application to linear regression

A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.     

Adaptation under probabilistic error for estimating linear functionals

The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of convex parameter spaces. In contrast to mean squared error it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic error. A general construction of such estimators is provided and examples are given to illustrate the general theory.     

线性等式约束下基本线性模型最佳线性无偏预测值的一些评论

In this paper, we give the representation of the best linear unbiased predictor(BLUP)of the new observations under M_r_f. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs(ordinary least squares estimators) and BLUEs(best linear unbiased estimators), under M_f and M_r_f, and the predictor, BLUP, under M_f continue to be the BLUP under M_r_f, respectively.     

Improvement of estimators in a linear regression problem with random errors in coefficients

Under consideration is the problem of estimating the linear regression parameter in the case when the variances of observations depend on the unknown parameter of the model, while the coefficients (independent variables) are measured with random errors. We propose a new two-step procedure for constructing estimators which guarantees their consistency, find general necessary and sufficient conditions for the asymptotic normality of these estimators, and discuss the case in which these estimators have the minimal asymptotic variance.