部分线性变系数模型的新复合分位数回归估计

针对部分线性变系数模型的参数估计问题,提出了一种新复合分位数回归估计方法.利用复合分位数回归法估计参数部分,局部非线性复合分位数回归法估计变系数函数部分,并在若干正则条件下,证明了常系数和变系数函数估计量具有较好的渐近正态性质.通过随机模拟和实例分析,验证了所提估计方法在有限样本下的良好表现,有效的证明了所提方法的优越...     

半参数回归模型独立情形的分离法估计

对半参数回归模型,用L2最佳逼近加矩估计的方法,推出其非参数部分的依L2与强相合联合收敛意义下的估计,及参数部分的强相合与相合渐近正态估计,并设计实行了一个模拟实验.     

函数型部分线性复合分位数回归模型的估计（英文）

本文研究函数型部分线性复合分位数回归模型的估计问题.我们采用函数型主成分分析方法分析斜率函数,回归样条逼近非参数函数.在相当宽松的条件下给出斜率函数和非参数函数的收敛速度.最后通过理论模拟和实例分析来评价我们提出的方法.     

基于众数回归的变系数部分非线性模型的稳健估计

针对变系数部分非线性模型,提出了一种稳健的基于众数回归的两阶段估计方法.首先,基于B-样条函数近似系数函数,利用QR正交分解技术构造了非线性模型,得到了参数的非线性最小二乘估计.其次,提出了变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

空间半参数变系数部分线性回归中的分位数估计

本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质.     

部分函数型线性可加分位数回归模型

文章结合可加分位数回归模型和函数型线性分位数回归模型,提出了部分函数型线性可加分位数回归模型.我们采用函数型主成分基函数逼近斜率函数,B-样条基函数逼近可加函数,提出了模型的估计方法;在一些基本的假设条件下,给出了斜率函数估计和可加函数估计的收敛速度;最后通过模拟计算和应用实例表明了所提方法的有效性.     

纵向数据下非参数带测量误差的部分线性变系数模型的估计

本文研究纵向数据下非参数部分带有测量误差的部分线性变系数模型的估计.利用B样条函数近似模型中的变系数函数,构造偏差修正的二次推断函数,得到模型中未知参数和变系数函数的估计.证明变系数函数估计量的相合性和参数估计量的渐近正态性.数值模拟和实例分析结果表明所提估计方法在有限样本下的有效性.     

广义函数型部分变系数混合模型的估计

将广义变系数回归模型与广义函数型线性回归模型相结合,提出了一种新的模型——广义函数型部分变系数混合模型.基于函数型主成分基和B-样条基的方法,通过最大化拟似然函数得到了未知函数的估计,并在一定的正则条件下得到了各估计量的收敛速度及预测精度.通过数值模拟展现了模型的可行性和优越性,最后将所建模型应用到Tecator数据说...     

函数型空间自回归模型的贝叶斯估计

函数型数据广泛地存在于社会的各个领域, 函数型数据分析也成为越来越热的统计研究方向. 经典的函数型回归模型一般假设响应变量是一个独立变量, 而在经济学, 环境科学等领域会经常遇到响应变量具有空间相依关系. 因此针对带有空间响应变量的部分函数型空间自回归模型, 基于函数型主成分分析和MCMC算法研究了模型的贝叶斯估计. 运用■表示定理来逼近函数型系数的思想, 以及应用Gibbs抽样和Metropolis-Hastings算法相结合的混合MCMC算法来获得模型中未知参数和函数型系数的贝叶斯估计结果. 最后通过模拟研究和对加拿大气温数据的实证分析来表明所提出的贝叶斯估计方法是可行有效的.     

同时估计回归函数零点及噪声参数

对未知的回归函数以 ARMA 型的误差得到量测时,本文以随机逼近型算法搜索回归函数的零点,同时以参数辨识算法估计噪声模型中的未知系数阵.本文证明了两种算法以概率1的收敛性.     

Effects of measurement error on a class of single-index varying coefficient regression models

This paper investigates the estimation in a class of single-index varying coefficient regression model when some covariates are contaminated with measurement errors. A bias-corrected least square procedure based on the observed data is proposed. By replacing the nonparametric single index part with a local linear approximation, an iterative algorithm for estimating the index parameter is proposed. More importantly, a special case is identified in which the naive procedure provides consistent estimates for the single index parameters. Large sample properties of the proposed estimators are established. The finite sample performance of the proposed estimators are evaluated by simulation studies.     

Efficient estimation of varying coefficient seemly unrelated regression model

In this paper, we propose a class of varying coefficient seemingly unrelated regression models, in which the errors are correlated across the equations. By applying the series approximation and taking the contemporaneous correlations into account, we propose an efficient generalized least squares series estimation for the unknown coefficient functions. The consistency and asymptotic normality of the resulting estimators are established. In comparison with the ordinary/east squares ones, the proposed estimators are more efficient with smaller asymptotical variances. Some simulgtlon＇studies and a real application are presented to demonstrate the finite sample performance of the proposed methods. In addition, based on a B-spline approximation, we deduce the asymptotic bias and variance of the proposed estimators.     

分位数变系数模型基于核光滑的变量选择

分位数变系数模型是一种稳健的非参数建模方法.使用变系数模型分析数据时,一个自然的问题是如何同时选择重要变量和从重要变量中识别常数效应变量.本文基于分位数方法研究具有稳健和有效性的估计和变量选择程序.利用局部光滑和自适应组变量选择方法,并对分位数损失函数施加双惩罚,我们获得了惩罚估计.通过BIC准则合适地选择调节参数,提出的变量选择方法具有oracle理论性质,并通过模拟研究和脂肪实例数据分析来说明新方法的有用性.数值结果表明,在不需要知道关于变量和误差分布的任何信息前提下,本文提出的方法能够识别不重要变量同时能区分出常数效应变量.     

随机变量的多项式最佳均方误差逼近

给出了一个随机变量关于另一个随机变量的 n次多项式最佳均方误差逼近公式,并分析了这种逼近的误差形式与大小.利用矩估计方法给出了这种逼近的回归系数的矩估计.     

Regression Density Estimation With Variational Methods and Stochastic Approximation

Regression density estimation is the problem of flexibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses finite mixture models and our article considers flexible mixtures of heteroscedastic regression (MHR) models where the response distribution is a normal mixture, with the component means, variances, and mixture weights all varying as a function of covariates. Our article develops fast variational approximation (VA) methods for inference. Our motivation is that alternative computationally intensive Markov chain Monte Carlo (MCMC) methods for fitting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three contributions. First, a VA for MHR models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation (SA) methods to perturb the initial solution to attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared with MCMC-based approaches are illustrated. These advantages are particularly compelling for time series data where repeated refitting for one-step-ahead prediction in model choice and diagnostics and in rolling-window computations is very common. Supplementary materials for the article are available online.     

平衡损失下回归系数的线性Minimax估计

在平衡损失函数下,主要研究回归系数的线性Minimax估计问题.通过分析平衡损失风险的极大极小性,得到了线性优化计类中回归函数的Minimax估计.在适当的假设下,证明了其唯一性.     

平衡损失下回归系数的最优线性无偏估计

在平衡损失函数下得到了回归系数的最优线性无偏估计,结果表明平衡损失下的最优线性无偏估计就是线性模型中回归系数的最小二乘估计.     

Coefficient estimation in a first-order nonlinear hyperbolic Cauchy problem

This paper deals with the estimation and approximation of coefficient function in a first-order, nonlinear, hyperbolic Cauchy problem. The estimation is accomplished by minimizing a functional which measures the error between a finite set of given observations and the corresponding values of the solution generated by the coefficient function. A class of admissible coefficient functions is defined, and it is proved that minimizing coefficient function always exists within this class. We also develop an approximation by a sequence of solutions of associated finite-dimensional minimization problems.     

Sparse Multivariate Regression With Covariance Estimation

We propose a procedure for constructing a sparse estimator of a multivariate regression coefficient matrix that accounts for correlation of the response variables. This method, which we call multivariate regression with covariance estimation (MRCE), involves penalized likelihood with simultaneous estimation of the regression coefficients and the covariance structure. An efficient optimization algorithm and a fast approximation are developed for computing MRCE. Using simulation studies, we show that the proposed method outperforms relevant competitors when the responses are highly correlated. We also apply the new method to a finance example on predicting asset returns. An R-package containing this dataset and code for computing MRCE and its approximation are available online.     

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.