Consistency of modified MLE in EV model with replicated observations

In case that replicated observations are available in some experimental points, the parameters estimation of one-dimensional linear errors-in-variables (EV) models was studied. Weak and strong consistency was proved under mild conditions.     

有重复观测时变系数线性结构关系EV模型的参数估计

利用重复观测数据和加权方法给出了有重复观测时变系数一维线性结构关系EV模型中的参数估计,证明了估计的弱相合性和强相合性．     

Estimation of partial linear error-in-response models with validation data

In this paper, an estimation theory in partial linear model is developed when there is measurement error in the response and when validation data are available. A semiparametric method with the primary data is used to define two estimators for both the regression parameter and the nonparametric part using the least squares criterion with the help of validation data. The proposed estimators of the parameter are proved to be strongly consistent and asymptotically normaal, and the estimators of the nonparametric part are also proved to be strongly consistent and weakly consistent with an optimal convergent rate. Then, the two estimators of the parameter are compared based on their empirical performances. Supported by NNSF of China (No. 10231030, No. 10241001) and a grant to the author for his excellent Ph.D. dissertation work in China.     

Linear EV model with replicate observations on independent variables

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.     

Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear EV Models

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.     

Strong consistency of M-estimates in linear models

The strong consistency of M-estimates of the regression coefficients in a linear model under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment condition. Especially, in some important circumstances, onlyE|ψ(e_k)|^q for some q > 1 is needed, where ψ{e_k} is some score function of random error.     

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.     

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。     

Consistent estimation of coefficients in measurement error models with replicated observations

For the estimation of coefficients in a measurement error model, the least squares method utilizing original observations and averaged observations over replications provides inconsistent estimators. Based on these, consistent estimators are formulated and asymptotic properties are analyzed.     

Existence of unbiased estimate of regression parameters in simple linear EV models

It is well known that for one-dimensional normal EV regression model X = x u,Y =α βx e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and βare not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and βunder some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and βexist, and the form of the MVUE of a and βare also given.     

Empirical likelihood for partial linear models

In this paper the empirical likelihood method due to Owen (1988,Biometrika,75, 237–249) is applied to partial linear random models. A nonparametric version of Wilks' theorem is derived. The theorem is then used to construct confidence regions of the parameter vector in the partial linear models, which has correct asymptotic coverage. A simulation study is conducted to compare the empirical likelihood and normal approximation based method. Research supported by NNSF of China and a grant to the first author for his excellent Ph.D. dissertation work in China. Research supported by Hong Kong RGC CERG No. HKUST6162/97P.     

随机截尾下污染数据部分线性模型的强相合估计

考虑一类新的污染数据部分线性模型,当受污染后的因变量被随机右截断时,就截断分布已知的情形,利用所获得截断观测数据构造了模型中的参数分量,非参数分量及污染系数的估计量,并在适当的条件下,证明了这些估计量的强相合性.     

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.     

CONSISTENCY OF LS ESTIMATOR IN SIMPLE LINEAR EV REGRESSION MODELS

Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.     

变系数线性EV模型参数的调整加权最小二乘估计及其渐近性质

研究当结构关系EV(errors-in-variables)模型的系数随某个实变量变化时,如何估计其系数,以及估计的性质如何．采用调整的加权最小二乘方法估计结构关系EV模型的变系数,证明在比较弱的条件下用这种方法得到的估计具有强相合性和渐近正态性,模拟研究表明所提估计性质良好．     

变系数EV模型基于核估计的误差方差估计

在利用核函数法和广义最小二乘法讨论变系数EV模型系数参数估计的基础上给出了其误差方差σ2的一种估计量(σ)2n,证明了所定义的估计量(σ)2n有很好的大样本性质.     

ASYMPTOTIC NORMALITY OF PARAMETERSESTIMATION IN EV MODEL WITH REPLICATEDOBSERVATIONS

1 IntroductionFOrnully the EV (Errors-ill-Vaiables) nrodel is just tlie regressiOli medel with both depen-dent aud iudependeut variables arc subject to error (see, fOr exan1ple, [21~[71 alid tlie literaturecited tl1ere). Collsiderillg tliat iu mauy practical aPplications, taking replicated observationspresellts lio esseutial dimculties. heuce can offer a couveuiellt choice in avoidillg artilicia1 as-sunWtions about tlie nlodel. This case was studied ill essay [11, in which estinators of a …     

Strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q×1 responses, bounded and fixed p×q regressors zi and general link function, under the most general assumption on the minimum eigenvalue of ∑in=1 ZiZi', the moment condition on responses as weak as possible and other mild regular conditions, we prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n, which converges to the true regression parameter β0. This result is an essential improvement over the relevant results in literature.     

半参数方差误差模型的估计

本文综合近邻权函数法及最小二乘法，用两阶段最小二乘估计的方法得到了半参数EV模型中参数的估计量及其强相合性，渐近正态性。同时也得到了非参数函数的估计量及其强相合性，一致强相合性。     

部分结构突变的线性面板模型的变点估计

Han Jiao;Xia Zhiming(School of Mathematics,Northwest University,Xi'an 710127,China)