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.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法

主要研究了部分线性变系数空间自回归模型的变量选择问题。结合拟最大似然方法、局部线性光滑方法以及一类非凸罚函数,提出了一个变量选择方法用于同时选择该模型的参数部分中重要解释变量和估计相应的非零参数。大量模拟研究表明,所提出的变量选择方法具有满意的有限样本性质,并且关于空间权矩阵的稀疏度、空间相关强度、系数函数的复杂度以及误差分布的非正态性非常稳健。特别地,当样本容量较大且罚函数选择合适时,即使解释变量的相关性较强或者模型中含有较多不重要解释变量,所提出的变量选择方法仍然具有比较满意的有限样本性质。通过分析波士顿房屋价格数据考察了所提出的变量选择方法的实际应用效果。

热转印系统色带传动过程张力分析与建模

为保证热转印过程中薄膜色带传动稳定进而实现高质量转印,建立正确的热转印色带传动张力模型十分关键。首先,研究了热转印色带传动系统组成及转印原理,并根据色带传动路径分辊间段、放卷段和收卷段3阶段对色带传动系统张力进行了建模与分析。然后,结合热转印色带卷材的黏弹性分析张力形成机制,改进了卷绕系统经典张力公式,建立了辊间段薄膜色带张力模型。针对传动系统的放卷区域,分析了摩擦对薄膜色带传动张力的影响,提出张力下降系数以评估张力损失。考虑色带张力非线性时变的特点,利用步进电动机负载模型求解收卷区域色带张力。最后,通过对比仿真与实验所得的色带张力变化曲线,验证了模型的准确性,为后续张力控制方案设计奠定了基础。

变系数部分非线性模型的分位数回归估计

研究纵向数据缺失下变系数部分非线性分位数回归模型的估计问题.利用逆概率加权法结合分位数回归给出参数估计和非参估计;在一定条件下,证明了所给估计量的渐近正态性;通过数值模拟,验证了所提方法的有效性.

基于加权复合分位数回归的变系数部分线性模型的稳健经验似然估计

研究了变系数部分线性模型的稳健经验似然推断问题。利用加权复合分位数回归以及经验似然方法,并结合基于矩阵QR分解的正交投影技术,对模型的参数分量提出了一种基于加权复合分数回归的经验似然估计方法。理论证明了提出的经验对数似然比函数渐近服从卡方分布,得到参数分量的置信区间。该估计方法中引入了基于矩阵QR分解的正交投影技术,保证对模型的参数分量进行估计时不会受到非参数分量估计精度的影响,因此具有较好的稳健性和有效性。

Variable Selection for Semiparametric Varying-Coefficient Partially Linear Models with Missing Response at Random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.

Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

Influence Diagnostics in Partially Varying-Coefficient Models

When a real-world data set is fitted to a specific type of models, it is often encountered that one or a set of observations have undue influence on the model fitting, which may lead to misleading conclusions. Therefore, it is necessary for data analysts to identify these influential observations and assess their impact on various aspects of model fitting. In this paper, one type of modified Cook＇s distances is defined to gauge the influence of one or a set observations on the estimate of the constant coefficient part in partially varying- coefficient models, and the Cook＇s distances are expressed as functions of the corresponding residuals and leverages. Meanwhile, a bootstrap procedure is suggested to derive the reference values for the proposed Cook＇s distances. Some simulations are conducted, and a real-world data set is further analyzed to examine the performance of the proposed method. The experimental results are satisfactory.

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.

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.

Identification of Non-Varying Coefficients in Varying-Coefficient Models

A partially varying-coefficient model is one of the useful modelling tools.In this model, some coefficients of a linear model are kept to be constant whilst the others areallowed to vary with another factor. However, rarely can the analysts know a priori whichcoefficients can be assumed to be constant and which ones are varying with the given factor.Therefore, the identification problem of the constant coefficients should be solved before thepartially varying-coefficient model is used to analyze a real-world data set. In this article, asimple test method is proposed to achieve this task, in which the test statistic is constructed asthe sample variance of the estimates of each coefficient function in a well-knownvarying-coefficient model. Moreover two procedures, called F-approximation and three-moment χ~2approximation, are employed to derive the p-value of the test. Furthermore, some simulations areconducted to examine the performance of the test and the results are satisfactory.

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

Inference on Varying-Coefficient Partially Linear Regression Model

The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.

摩擦因数时变的节点外啮合齿轮系动力学分析

以外啮合节点后啮合单级齿轮传动系统为研究对象,建立了系统六自由度非线性动力学模型,考虑了时变啮合刚度、时变齿面摩擦、载荷在啮合区动态分配以及齿侧间隙的影响。采用能量法计算了时变啮合刚度。基于弹流润滑(Elasto-hydrodynamic lubrication,EHL)理论计算了时变摩擦因数,与库伦摩擦模型进行了对比分析,得到了齿轮副非线性振动方程,同时采用数值方法求解了系统的动力学微分方程组,得到了系统的时域动态响应和相图,并分析了系统的动力学特性。

响应变量随机缺失下的变系数部分线性模型的经验似然推断

本文考虑了响应变量随机缺失下的变系数部分线性模型的估计问题。利用经验似然方法,给出了参数部分的调整经验似然比函数,证明其渐近服从标准卡方分布。进而构造了参数部分的置信域,得到了其极大经验似然估计的最优参数收敛速度和渐近半参数有效界。模拟结果表明调整经验似然方法优于未调整的经验似然方法。

部分线性变系数模型的随机约束岭估计

作为变系数模型和部分线性模型的推广,部分线性变系数模型近年来得到越来越多的关注.本文考虑该模型在线性部分自变量存在多重共线性并且参数分量附加有随机约束条件时的估计问题.基于profile最小二乘技术以及岭估计和混合估计方法,构造参数分量的profile混合岭估计,并且研究所提估计量的渐近性质.最后利用数值模拟验证所提估计方法的有效性.

部分线性变系数模型Backfitting估计的渐近性质

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用广泛的数据分析模型.利用Backfitting方法拟合这类特殊的可加模型,可得到模型中常值系数估计量的精确解析表达式,该估计量被证明是n^(1/2)相合的.最后通过数值模拟考察了所提估计方法的有效性.

部分线性变系数模型中误差方差的估计(英文)

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类在建模中应用非常广泛的模型.本文基于Profile最小二乘方法给出了模型中误差方差的估计并证明了该估计的渐近正态性.最后通过数值模拟验证了我们所提估计方法的有效性.