STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

基于曲线拟合误差估计的阻抗优化识别方法

在雷达系统、舰船系统、数据中心等大型复杂系统中,供配电系统变流器端口阻抗信息的完整、快速、准确获取,是研判系统可靠性的重要基础。现有研究大都使用分段线性拟合值方法进行阻抗识别,不仅需要大量阻抗测量才能获得完整的阻抗特性,并且可能因过度测量而对系统的正常运行造成干扰。针对这些问题,从阻抗特性曲线的非线性拟合入手,提出一种“非线性曲线拟合、全局误差估计、优选测量点频率”的阻抗识别方法,实现基于曲线拟合误差估计的测量点优化选择,以较少阻抗测量代价获取宽频带阻抗特性。与现有的方法相比,所提方法更有助于测量点的合理选择、阻抗谐振峰的准确识别,从而更高效地实现宽频带阻抗的识别,为复杂供配电系统运行状况的研判提供可靠依据。算例仿真证实了所提方法的有效性。

Statistical Inference for Partially Linear Regression Models with Measurement Errors

在这篇论文，作者为某 covariates 与错误被测量的部分线性的回归模型调查统计推理的三个方面。第一，一个带宽选择过程被建议，它是基于差别的技术的联合；GCV 方法。第二，一个 goodness-of-fit 测试过程被建议，它是概括可能性技术的延期。第三，为参量的部分的一个可变选择过程被提供基于非凹面 penalization；改正的侧面最不摆平。作为一样“可变选择经由非，凹面惩罚了可能性；它的神谕性质“(J。Amer。统计员。Assoc， 96， 2001， 1348 1360 ) ，产生评估者与规则化参数的一种合适的选择有一个神谕性质，这被显示出；惩罚功能。模拟研究被进行说明建议过程的有限样品表演。

Partially Linear Single-Index Model in the Presence of Measurement Error

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

基于自适应小波回声神经网络的光纤陀螺测角仪温度误差补偿技术

基于光纤陀螺的测角仪可以实现对各项角运动参数的一体化动态精密测量,但在实际应用中,光纤陀螺测角仪受到温度变化的影响,导致测量精度下降。针对这一问题,本文提出了一种基于自适应小波回声神经网络的光纤陀螺测角仪温度误差补偿技术。为了提高温度误差建模的进度,提高传统神经网络的逼近能力,通过自适应前向线性预测滤波器对建模用测角仪温度漂移数据进行预处理,并采用自适应小波回声神经网络建立温度漂移模型,能够避免传统神经网络结构设计的盲目性和局部最优等问题,增强了网络学习能力和泛化能力,并利用自适应律代替神经网络梯度进行网络训练,提升神经网络的逼近精度和收敛速度。实验结果表明,该模型可以提高光纤陀螺测角仪的测量精度和环境适应性,为光纤陀螺测角仪的性能优化和实际应用提供了可靠的技术支撑。

水准测量中尺度比参数的附加系统参数的Partial EIV模型解法

针对目前水准测量中尺度比参数的附加系统参数的平差模型,本文对模型进行重构,提出尺度比参数的附加系统参数的partial errors-in-variables(Partial EIV)模型,给出总体最小二乘准则下的解算公式及迭代算法。实际算例和模拟数据结果表明,本文方法与传统方法在处理尺度比参数为附加系统参数时的效果基本一致,并给出相关的理论依据。

部分线性变系数模型的贝叶斯分位数回归

针对部分线性变系数模型的参数估计问题,采用B样条方法逼近非参数部分的未知光滑函数,进而利用非对称拉普拉斯分布实现贝叶斯分位数回归,并基于Gibbs抽样推导出所有未知参数的后验分布,通过数值模拟比较分析了贝叶斯分位数回归与分位数回归参数估计的优劣,结果表明,在均方误差准则下,贝叶斯分位数回归的估计效果更优。最后,通过实例分析说明了所提方法的有效性。

Testing Serial Correlation in Partially Linear Additive Models

As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.

Corrected empirical likelihood for a class of generalized linear measurement error models

Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.

TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.

Efficient Statistical Inference for Partially Nonlinear Errors-in-Variables Models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.

Corrected-loss estimation for Error-in-Variable partially linear model

We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.

Empirical Likelihood for Partially Linear Models Under Negatively Associated Errors

这份报纸建议使用 blockwise 在否定地联系的错误下面在一个部分线性的模型为回归向量构造信心区域的实验可能性的(EL ) 方法。这被显示出 blockwise EL 比率统计数值为 asymptotically， 2 散布了。结果被用来获得一个基于 EL 的信心区域为。建议信心区域的有限样品表演上的模拟研究的结果被报导。

TWO-STEP ESTIMATORS IN PARTIAL LINEAR MODELS WITH MISSING RESPONSE VARIABLES AND ERROR-PRONE COVARIATES

有失踪的反应变量和错误容易的 covariates 的一个部分线性模型被考虑。归罪途径被开发估计回归系数和 nonparametric 功能。建议参量的评估者被显示 asymptotically 正常，并且为 nonparametric 部分的评估者被证明以最佳的率收敛。到为回归系数和 nonparametric 功能的构造信心区域，分别地，作者也建议 empirical-likelihood-based 统计并且调查实验可能性的比率的限制分布。模拟学习被进行为建议评估者比较有限样品行为。到爱滋病数据集的一个应用程序被说明。

Asymptotic Properties of Wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

附加一次和二次等式约束的Partial-EIV模型及相应算法

研究了附加一次和二次等式约束的Partial-EIV模型,推导了加权整体最小二乘估计准则下相应的计算公式,并讨论了仅附加一次等式约束的Partial-EIV模型和仅附加二次等式约束的Partial-EIV模型。通过正交线性回归和平面坐标转换两个算例进行实验,将新算法与已有的附加等式约束的EIV模型的方法进行了对比,发现文中方法计算效率更高,且适用于结构化EIV模型的求解。

Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters

This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.

BLUP Estimation of Linear Mixed-effects Models with Measurement Errors and Its Applications to the Estimation of Small Areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.

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

Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.

Statistical Inferences in a Partially Linear Model with Autoregressive Errors

In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.