变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

纵向数据变系数模型中的减元估计法

纵向数据变系数模型常应用于传染病学、生物医学和环境科学等领域. 本文提出了一种称为减元估计法的方法来估计模型中的未知函数和它们的导数. 减元估计法既适用于系数函数具有相同光滑度的情形, 也适用于系数函数具有不同光滑度的情形; 既适用于变量不依赖于时间的情形, 也适用于变量依赖于时间的情形. 给出了一般条件下估计量的局部渐近偏差、方差和渐近正态性, 并且渐近性结果显示: 当系数函数具有不同的光滑度时, 减元估计量的渐近方差比现有方法得到的估计量的渐近方差要少. 本文还通过 Monte Carlo 模拟研究了估计量的有限样本性质.     

半变系数模型PLS估计的渐近正态性

半变系数模型在统计建模中具有重要的应用．最近几年，人们提出了许多方法来估计其常系数和函数系数，但是估计的渐近性质还没有被系统的研究．本文介绍了半变系数模型的PLS估计，在Fan和Huang对常系数渐近性质研究的基础上，给出了函数系数的渐近正态性。     

误差相关的半变系数模型的估计

本文在误差相关的情况下, 研究半变系数模型的估计, 通过改进PLS估计, 给出了函数系数和常数系数的估计, 证明了估计的渐近正态性; 最后, 模拟研究说明了所提方法的有效性.     

纵向数据变系数回归模型小波估计的渐近性质

考虑纵向数据下的变系数回归模型y_(ij)=x_(ij)~Tθ(t_(ij))+e_(ij)i=1,2,…,n j=1,2,…,m.利用小波光滑和加权最小二乘方法,分别研究了模型中未知参数θ(·)的小波估计θ(·)和误差方差σ~2的小波估计σ~2,在适当的条件下,证明了θ的强相合性,强相合速度,并得到θ和σ~2的渐近正态性.     

变系数模型小波估计的渐近性

变系数模型是线性模型的有用推广,它允许回归系数是某个变量的函数,近年来在统计分析中得到广泛的应用.文中研究回归变量都是随机时的变系数模型,提出运用小波的方法估计变系数模型中的函数系数,并在较弱的条件下得到了变系数模型小波估计的渐近正态性.     

变系数模型的小波估计

变系数模型是近年来文献中经常出现的一种统计模型.本文主要研究了变系数模型的估计问题,提出运用小波的方法估计变系数模型中的系数函数,小波估计的优点是避免了象核估计、光滑样条等传统的变系数模型估计方法对系数函数光滑性的一些严格限制. 并且,我们还得到了小波估计的收敛速度和渐近正态性.模拟研究表明变系数模型的小波估计有很好的估计效果.     

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.     

变系数模型中的一步估计法

提出一步估计方法用以估计变系数模型中具有不同光滑度的未知函数. 在这一方法中, 不同阶的多项式用来逼近不同光滑度的未知函数. 由于只使用一次极小化, 所需计算量要比现有的两步方法少得多. 一步估计量被证明达到了最优收敛速度, 而且, 这一性质是在比两步估计法更弱的条件下得到的. 更重要的是, 由于只执行一次极小化, 估计量的所有渐近性质, 不仅是渐近偏差、方差, 而且渐近分布都能推出. 渐近分布将在统计推断中起着重要作用.     

One-step estimation for varying coefficient models

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.     

Robust estimation for varying index coefficient models

Varying index coefficient models (VICMs) proposed by Ma and Song (J Am Stat Assoc, 2014. doi: 10.1080/01621459.2014.903185) are a new class of semiparametric models, which encompass most of the existing semiparametric models. So far, only the profile least squares method and local linear fitting were developed for the VICM, which are very sensitive to the outliers and will lose efficiency for the heavy tailed error distributions. In this paper, we propose an efficient and robust estimation procedure for the VICM based on modal regression which depends on a bandwidth. We establish the consistency and asymptotic normality of proposed estimators for index coefficients by utilizing profile spline modal regression method. The oracle property of estimators for the nonparametric functions is also established by utilizing a two-step spline backfitted local linear modal regression approach. In addition, we discuss the bandwidth selection for achieving better robustness and efficiency and propose a modified expectation–maximization-type algorithm for the proposed estimation procedure. Finally, simulation studies and a real data analysis are carried out to assess the finite sample performance of the proposed method.     

Reducing component estimation for varying coefficient models with longitudinal data

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.     

Efficient estimation of longitudinal data additive varying coefficient regression models

Acta Mathematicae Applicatae Sinica, English Series - We consider a longitudinal data additive varying coefficient regression model, in which the coefficients of some factors (covariates) are...     

Concave group methods for variable selection and estimation in high-dimensional varying coefficient models

The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high-dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator (Lasso) selects a model whose dimension is comparable to the underlying model, regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty (MCP) has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.     

Statistical estimation in varying coefficient models with surrogate data and validation sampling

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.     

Variable selection for fixed effects varying coefficient models

We consider the problem of variable selection for the fixed effects varying coefficient models.A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.     

B-spline estimation for varying coefficient regression with spatial data

This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the u...     

半参数变系数部分线性模型的统计推断

本文在多种复杂数据下, 研究一类半参数变系数部分线性模型的统计推断理论和方法. 首先在纵向数据和测量误差数据等复杂数据下, 研究半参数变系数部分线性模型的经验似然推断问题, 分别提出分组的和纠偏的经验似然方法. 该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难. 其次在测量误差数据和缺失数据等复杂数据下, 研究模型的变量选择问题, 分别提出一个“纠偏” 的和基于借补值的变量选择方法. 该变量选择方法可以同时选择参数分量及非参数分量中的重要变量, 并且变量选择与回归系数的估计同时进行. 通过选择适当的惩罚参数, 证明该变量选择方法可以相合地识别出真实模型, 并且所得的正则估计具有oracle 性质.