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...     

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.     

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.     

Bayesian‐type count data models with varying coefficients: estimation and testing in the presence of overdispersion

In this paper we study varying‐coefficient models for count data. A Bayesian approach is taken to model the variability of the regression parameters. Based on a Kalman filter procedure the varying coefficients are estimated as the mode of the posterior distribution. All hyperparameters, including an overdispersion parameter in the negative binomial varying‐coefficient model (NBVC), are estimated as ML‐estimators using an EM‐type algorithm. A bootstrapping test of the fixed‐coefficient hypothesis against a varying‐coefficient alternative is proposed, which is evaluated running a simulation study. The study shows that the choice of a suitable count data model is of special importance in the framework of varying‐coefficient models. The methodology is illustrated analysing the determinants of the number of individual doctor visits. Copyright © 2001 John Wiley & Sons, Ltd.     

Kernel Smoothing Estimation for Varying Coefficient EV Models with Longitudinal Data

Varying coefficient EV models with longitudinal data are considered. The local bias-corrected kernel estimators for the unknown coefficient functions are proposed. It is shown that the proposed estimators are asymptotically normal under some suitable conditions, and hence it can be used to construct the pointwise confidence regions of the coefficient functions. The finite-sample properties of the proposed procedures are studied through a simulation study.     

Mixtures of semiparametric varying coefficient models for longitudinal data with nonignorable dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.     

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.     

Estimating population proportions in the presence of missing data

This paper discusses the estimation of a population proportion in the presence of missing data and using auxiliary information at the estimation stage. A general class of estimators, which make efficient use of the available information, are proposed. Some theoretical properties of the proposed estimators are analyzed, and they allow us to find the optimal value for the proposed class in the sense of minimal variance. The optimal estimator is thus more efficient than the customary estimator. Results derived from a simulation study indicate that the proposed optimal estimator gives desirable results in comparison to alternative estimators.     

A Class of Robust Principal Component Vectors

This paper is concerned with a study of robust estimation in principal component analysis. A class of robust estimators which are characterized as eigenvectors of weighted sample covariance matrices is proposed, where the weight functions recursively depend on the eigenvectors themselves. Also, a feasible algorithm based on iterative reweighting of the covariance matrices is suggested for obtaining these estimators in practice. Statistical properties of the proposed estimators are investigated in terms of sensitivity to outliers and relative efficiency via their influence functions, which are derived with the help of Stein's lemma. We give a simple condition on the weight functions which ensures robustness of the estimators. The class includes, as a typical example, a method by the self-organizing rule in the neural computation. A numerical experiment is conducted to confirm a rapid convergence of the suggested algorithm.     

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.     

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.     

核实数据下非线性半参数EV模型的估计

本文研究了核实数据下的协变量带有测量误差的非线性半参数EV模型.在不假定测量误差结构的情形下,利用最小二乘方法和核光滑技术,构造了非线性函数中未知参数的两种估计,证明了未知参数估计的渐近正态性.通过数值模拟说明所提估计方法在有限样本下的有效性.     

Determination of the relaxation and retardation spectra – a view from the up-to-date signal processing perspective

The problem of determination of relaxation and retardation spectra (RRS) is considered from the viewpoint of up-to-date signal processing. It is shown that the recovery of RRS represents the Mellin deconvolution problem, which transforms into the Fourier deconvolution problem for data on a logarithmic time or frequency scale, where it can also be treated as the inverse filtering problem. On this basis, discrete deconvolution (inverse) filters operating with geometrically sampled data are proposed to use as RRS estimators. Appropriate frequency responses and algorithms are derived for estimating RRS from eight different material functions. The noise amplification coefficient is suggested to use as a measure for quantifying the degree of ill-posedness and illconditioness of the RRS recovery problem and algorithms. A methodology is developed for designing RRS estimators with a desired noise amplification, producing maximum accurate spectra for available limited input data. Practical algorithms for determining RRS are proposed, and their performance is studied. The algorithms suggested are compared with the so-called moving-average formulae. It is demonstrated that the minimum frequency range for recovering the point estimate of a relaxation spectrum depends on the allowable noise amplification (the degree of ill-conditioness) and is in no way limited by 1.36 decades, as it is stated by the sampling localization theorem.     

Probability density estimation for survival data with censoring indicators missing at random

In this paper, some nonparametric approaches of density function estimation are developed when censoring indicators are missing at random. A conditional mean score based estimator and a mean score estimator are suggested, respectively. The two estimators are proved to be asymptotically normal and uniformly strongly consistent. The bandwidth selection problem is also discussed. A simulation study is conducted to compare finite-sample behaviors of the proposed estimators.     

扩散模型中扩散系数的非参数组合估计

为了提高扩散系数估计的准确度, 我们利用动态组合时间域与状态域信息提出一个新的组合估计量. 我们发现所提组合估计量能有效估计扩散模型的扩散系数, 正如在本文中模拟所示. 在一定的条件下, 建立了估计量的渐进正态性, 并证明了时间域估计量与状态域估计量是渐进独立的. 大量的模拟展示了所提组合估计量优于单域估计量, 也优于本文所提估计量.     

比类型估计量在数量特征随机化回答技术中的应用

本文在数量特征随机化回答技术中当变异系数、偏度系数、峰度系数已知时,对总体均值提出了一系列比类型估计量,并且在一定条件下,证明了这些估计量优于Gupta et al.提出的估计量。     

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.     

因变量缺失下部分线性变系数变量含误差模型的估计

该文主要考虑部分线性变系数模型在自变量含有测量误差以及因变量存在缺失情形下的估计问题.基于Profile最小二乘技术,针对参数分量和非参数分量提出了多种估计方法.第一种估计方法只利用了完整观测数据,而第二种和第三种估计方法分别利用了插补技术和替代技术.参数分量的所有估计被证明是渐近正态的,非参数分量的所有估计被证明和一般非参数回归函数的估计具有相同的收敛速度.对于因变量的均值,构造了两类估计并证明了它们的渐近正态性.最后,通过数值模拟验证了所提方法.     

变量为区间截断数据时回归模型的参数估计(英文)

在假设自变量X的分布为离散未知分布且样本为区间截断数据而因变量Y是可观察的情况下,利用EM方法得到了回归参数的极大似然估计,在一定的条件下估计量的分布为渐近正态的.     

PARAMETER ESTIMATION IN LINEAR REGRESSION MODELS FOR LONGITUDINAL CONTAMINATED DATA

The parameter estimation and the coefficient of contamination for the regression models with repeated measures are studied when its response variables are contaminated by another random variable sequence. Under the suitable conditions it is proved that the estimators which are established in the paper are strongly consistent estimators.