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.     

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.     

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。     

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．     

半变系数模型改进的轮廓最小二乘估计

针对半变系数模型,在局部线性拟合轮廓最小二乘估计方法的基础上将关于变系数函数的局部线性拟合改进为局部非线性拟合,得到半变系数模型改进的轮廓最小二乘估计,进一步讨论了常值系数的渐进正态性.     

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.     

部分线性模型中估计的渐近正态性

考虑回归模型其中是未知函数，（ｘ＿ｉ，ｔ＿ｉ，ｕ＿ｉ）是固定非随机设计点列，β是待估参数，ｅ＿ｉ是随机误差。基于ｇ（·）及ｆ（·）的一类非参数估计（包括常见的核估计和近邻估计），我们构造了β的加权最小二乘估计，并证得了最小二乘估计和加权最小二乘估计的渐近正态性。     

相依样本下条件中位数估计的渐近正态性

文中设｛（Ｘｎ，Ｙｎ）：ｎ≥｝为严平稳ρ－相依随机变量列，出于稳健角度，给出了Ｙ关于Ｘ回归中位Ｌ１－模估计θｈ（ｙ│ｘ），在适当条件下证明了θｈ（ｙ│ｘ）的渐近正态性。     

删失数据下半变系数模型估计的渐近正态性

半变系数回归模型是变系数回归模型的有效推广,已获得了广泛的应用. 本文在响应变量随机删失下对其进行讨论,给出常系数和函数系数的估计, 并证明了该估计的渐近正态性.     

半变系数模型的变窗宽和一步局部M-估计

讨论了半变系数模型的变窗宽一步局部M-估计.用一步局部M-估计给出了未知函数的估计,用平均法给出了未知参数的估计,并在其中嵌入一个变窗宽加以提高,得到了未知函数和未知参数的渐近正态性.     

A robust and efficient estimation method for single-index varying-coefficient models

A new estimation procedure based on modal regression is proposed for single-index varying-coefficient models. The proposed method achieves better robustness and efficiency than that of Xue and Pang (2013). We establish the asymptotic normalities of proposed estimators and evaluate the performance of the proposed method by a numerical simulation.     

Generalized profile LSE in varying-coefficient partially linear models with measurement errors

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, ··· , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.     

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.     

Variable selection for single-index varying-coefficient model

We consider the problem of variable selection for single-index varying-coefficient model, and present a regularized variable selection procedure by combining basis function approximations with SCAD penalty. The proposed procedure simultaneously selects significant covariates with functional coefficients and local significant variables with parametric coefficients. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. The proposed method can naturally be applied to deal with pure single-index model and varying-coefficient model. Finite sample performances of the proposed method are illustrated by a simulation study and the real data analysis.     

Asymptotic normality of wavelet estimator in heteroscedastic regression model

The following heteroscedastic regression model Y_i=g(x_i) σ_ie_i(1≤i≤n)is considered,where it is assumed thatσ_i~2=f(u_i),the design points(x_i,u_i)are known and nonrandom,g and f are unknown functions.Under the unobservable disturbance e_i form martingale differences,the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.     

On stochastic estimation

We consider a local random searching method to approximate a root of a specified equation. If such roots, which can be regarded as estimators for the Euclidean parameter of a statistical experiment, have some asymptotic optimality properties, the local random searching method leads to asymptotically optimal estimators in such cases. Application to simple first order autoregressive processes and some simulation results for such models are also included.     

Parameter estimation in linear filtering

Suppose on a probability space (Ω, F, P), a partially observable random process (x_t, y_t), t ≥ 0; is given where only the second component (y_t) is observed. Furthermore assume that (x_t, y_t) satisfy the following system of stochastic differential equations driven by independent Wiener processes (W₁(t)) and (W₂(t)): dx_t=−βx_tdt+dW₁(t), x₀=0, dy_t=αx_tdt+dW₂(t), y₀=0; α, β∞(a,b), a>0. We prove the local asymptotic normality of the model and obtain a large deviation inequality for the maximum likelihood estimator (m.l.e.) of the parameter θ = (α, β). This also implies the strong consistency, efficiency, asymptotic normality and the convergence of moments for the m.l.e. The method of proof can be easily extended to obtain similar results when vector valued instead of one-dimensional processes are considered and θ is a k-dimensional vector.     

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB ³ _p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error. Project supported by Doctoral Programme Foundation, the National Natural Science Foundation of China (Grant No. 19871003) and Natural Science Fundation of Heilongjiang Province, China.     

删失数据下的变系数回归模型

研究了删失数据下的变系数回归模型．通过数据变换,利用局部多项式方法,给出了系数函数的局部加权最小二乘估计．证明了该估计的渐近偏差和渐近方差,同时获得了该估计的渐近正态性．     

Nonlinear wavelet density estimation with censored dependent data

In this paper, we provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet estimator of survival density for a censorship model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary and α‐mixing sequence. This asymptotic MISE expansion, when the density is only piecewise smooth, is same. However, for the kernel estimators, the MISE expansion fails if the additional smoothness assumption is absent. Also, we establish the asymptotic normality of the nonlinear wavelet estimator. Copyright © 2011 John Wiley & Sons, Ltd.