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.     

变系数模型变窗宽和一步局部M-估计

用变窗宽和一步局部M-估计对变系数模型的系数参数进行估计,得到了估计的渐近正态性.     

变窗宽和一步局部M-估计 *

研究稳健的变窗宽局部线性回归 .所提出的方法继承了局部多项式回归的优点并且克服了最小二乘方法缺乏稳健性的缺点 .变窗宽的使用提高了所得到的局部M- 估计的可塑性并使得它们能成功地处理空间非齐性曲线、异方差性及非均匀设计密度 .在合适的正规条件下 ,所提出的估计是存在的且是渐近正态的 .基于稳健的估计方程 ,引进了一步局部M- 估计以减少计算负担 .只要初始估计足够好 ,一步局部估计将具有与整个迭代的M- 估计相同的渐近分布 .换句话说 ,一步局部M- 估计显著地减少整个迭代M- 估计的计算负担而不降低其执行效果 .模拟也说明了这个事实.     

p混合过程下变窗宽局部M-估计的强相合性

考虑到在实际应用中,运用变窗宽局部M-估计进行非参数估计时,所收集到的数据有时并非独立样本,而可能是一些混合样本.因此,本文就观测数据为ρ混合过程的条件下,讨论了变窗宽局部M-估计的强相合性,并给出两个具有较弱假设条件的定理.     

变系数联立模型的局部线性广义矩变窗宽估计

在随机设计条件下,提出了一类变系数联立模型,运用局部线性广义矩变窗宽估计,对模型的变系数进行了估计,研究了估计量的大样本性质.利用概率论中大数定律和中心极限定理,证明了估计量的大样本性质,局部线性广义矩变窗宽估计具有相合性和渐进正态性.     

部分线性回归模型变窗宽一步局部M-估计

讨论了部分线性回归模型的变窗宽一步局部M-估计.用一步局部M-估计给出未知函数的估计,用平均方法给出参数估计.进一步通过两个引理证明一步M-估计的渐近正态性.所提出的方法继承了局部多项式的优点并且克服了最小二乘法缺乏稳健性的缺点.     

基于变系数模型的自适应分位回归方法

提出了变系数模型条件分位估计的一种新方法.变系数模型已经成为经济学、流行病学、纵向数据和医学领域处理高维数据的有力工具.该模型有助于探测数据的动态特征、降低模型偏差、避免高维灾难,同时便于解释.尽管关于变系数模型条件均值的估计已经有很多文章,但关于变系数模型条件分位的估计方面的文章相对较少.文中提出了一种有效的适应性分位回归方法来诊断出齐性邻域,进行局部自适应窗宽选择和局部线性逼近,同时给出了估计量的风险界和最优窗宽的自动选择准则.模拟研究说明了所提出估计方法的效果.     

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.     

树结构变窗宽局部多项式拟合方法

变窗宽局部多项式模型是探索被估计曲线复杂变化结构的有力工具,其关键思想在于针对不同变化模式的数据区间选择不同窗宽参数进行拟合.基于回归树模型提出一种变窗宽多项式拟合方法,利用回归树的分类功能识别具有不同变化结构的数据区间,在每个子区间上独立选取最优窗宽,通过局部多项式回归实现复杂结构曲线的变窗宽拟合.随机模拟的结果表明,回归树能够有效识别具有不同变化模式的数据区间,变窗宽局部多项式拟合均方误差小,具有计算高效、结果易解释的特点.     

Variable bandwidth and one-step local M-estimator

A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.     

Data-driven local bandwidth selection for additive models with missing data

This paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable. Specifically in the case of additive models estimated by the Backfitting algorithm with local polynomial smoothers [1]. Three estimators are presented, one based on the available data and two based on a complete sample from imputation techniques. We also develop a data-driven local bandwidth selector based on a Wild Bootstrap approximation of the mean squared error of the estimators. The performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments.     

Local adaptive smoothing in kernel regression estimation

We consider nonparametric estimation of a smooth function of one variable. Global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method for selecting local smoothing parameters which takes into account sparseness and adapts to local curvature. A Bayesian type argument provides an initial smoothing parameter which adapts to the local sparseness of the covariate and provides the basis for local bandwidth selection procedures which further adjust the bandwidth according to the local curvature of the regression function. Simulation evidence indicates that the proposed method can result in reduction of both pointwise mean squared error and integrated mean squared error.     

改进的函数系数自回归建模方法对上海股市实证分析

函数系数自回归模型(FAR)是一类更具有适应性的模型。本文利用函数系数自回归模型对上海股市日收益率进行建模及短期预测,改进现有建模对带宽、模型的依赖变量以及阶数确定方法。并与上海股市日收益率的自回归模型结果进行了比较,结果表明改进的函数系数模型具有很好的预测能力。     

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.     

Local smoothing regression with functional data

Kernel estimates of a regression operator are investigated when the explanatory variable is of functional type. The bandwidths are locally chosen by a data-driven method based on the minimization of a functional version of a cross-validated criterion. A short asymptotic theoretical support is provided and the main body of this paper is devoted to various finite sample size applications. In particular, it is shown through some simulations, that a local bandwidth choice enables to capture some underlying heterogeneous structures in the functional dataset. As a consequence, the estimation of the relationship between a functional variable and a scalar response, and hence the prediction, can be significantly improved by using local smoothing parameter selection rather than global one. This is also confirmed from a chemometrical real functional dataset. These improvements are much more important than in standard finite dimensional setting.     

我国宏观经济非参数联立模型的局部线性工具变量变窗宽估计

联立方程模型在经济政策制定、经济结构分析和预测方面起重要作用，目前关于非参数计量经济模型的研究主要停留在单方程模型上，而联立方程模型的研究在国际上刚刚起步，本将非参数回归模型的局部线性估计方法与传统联立方程模型估计方法相结合，首次提出了非参数计量经济联立模型的局部线性工具变量变窗宽估计并应用于我国宏观经济非参数联立模型，结果表明：我国宏观经济非参数联立模型优于线性联立模型且线性模型将造成不必要的人为设定误差；对于非参数联立模型，局部线性工具变量变窗宽估计优于局部线性估计。