非参数自回归函数的有限元估计及其收敛速度

针对局部方法不能给出所拟合模型的简单的显式表达式,而且拟合和预报的计算量较大,本文考虑一种估计非参数自回归函数的全局有限元方法。该方法不但能克服上述局部方法之不足,而且在一定情形下优于多项式样条方法。在α-混合条件下得出了非参数自回归函数有限元估计的收敛速度,同时给出了利用AIC准则自动选择结点个数的数据追赶法,模拟算例说明了有限元估计方法的可行性。     

局部线性回归模型的半参估计

针对局部线性估计方法收敛速度较慢且对窗宽选择不稳健的问题,本文提出一种改进的局部线性半参估计方法。首先,选择不同窗宽作相应的局部线性估计,然后利用这些估计构造参数回归模型,由此给出回归函数的参数估计。相对于局部线性估计,新方法在不改变方差阶的情况下,将估计偏差的阶由h2减小至h4,最优均方收敛速度提高至O(n?89),且对窗宽选择稳健。模拟研究验证了新方法的有效性。     

矩阵损失下线性混合模型中的局部线性Minimax估计

本文研究了一般线性混合模型中固定效应和随机效应的线性组合的Minimax估计问题.在矩阵损失函数下,考虑了这个组合的线性估计在线性估计类中的局部极小极大性.关于适当的假设,得到了线性可估函数的唯一局部线性Minimax估计.     

部分线性模型中参数分量与非参数分量估计的收敛速度

对于部分线性回归模型,基于未知函数 ｆ （·） 与 ｇ （·） 分别取一类核估计和最近邻估计,文中构造了参数β的最小二乘估计β和加权最小二乘估计β,获得了参数β估计量的渐近正态性与函数ｇ （·） 估计量的最优弱收敛速度。     

自变量含有类型变量的线性回归模型的树方法

给出了求解自变量含有类型变量的线性回归模型的树方法。它是一个非参数方法。讨论了修剪树对参数估计和预测的影响，给出了通过修剪树提高参数估计和预测精度的充要条件。     

半参数回归模型拟极大似然估计的弱相合性

本文考虑一类固定设计的半参数回归模型,其误差为一阶自回归时间序列。用权函数及拟极大似然估计方法得到了一些参数及非参数的拟极大似然估计量,在适当的条件下,研究了它们的弱相合性,从而丰富了该类半参数回归模型的估计理论与方法。     

浅析核密度估计方法

1．核密度估计概念 kernel density estimation是在概率论中用来估计未知的密度函数,属于非参数检验方法之一,由Rosenblart（1955）和EmanuelParzen（1962）提出,又名Parzen窗（Parzenwindow）。Ruppert和Cline基于数据集密度函数聚类算法提出修订的核密度估计方法。由给定样本点集合求解随机变量的分布密度函数问题是概率统计学的基本问题之一。解决这一问题的方法包括参数估计和非参数估计。参数估计又可分为参数回归分析和参数判别分析。在参数回归分析中,人们假定数据分布符合某种特定的性态,如线性、可化线性或指数性态等,然后在目标函数族中寻找特定的解,即确定回归模型中的未知参数。     

采用线性回归方法的发动机活塞参数优化设计

活塞是发动机的重要零件,一般的活塞参数优化方法采用反复的实验、数据分析、参数改进,最终确定其主要参数.这种方法效率低,花费大量的人力与物力.作者提出了基于线性回归实现活塞主要参数优化设计的方法,即建立回归模型分析现有的成熟发动机和活塞参数,找出发动机参数与活塞参数之间的相关函数,利用这些函数并根据发动机的要求进行活塞主要参数的设计.     

多类型复发事件下的加性乘积比率回归模型

本文基于多类型复发事件数据,研究了半参数加性乘积比率回归模型的统计问题。利用现代经验过程理论与方法,给出了该模型中未知参数和非参数函数的一种估计方法,并证明了这些估计的相合性和渐近正态性。     

纵向数据半参数回归模型估计的强相合性

本文考虑如下纵向数据半参数回归模型:yij=x'ijβ g(tij) eij。基于最小二乘法和一般的非参数权函数方法给出了模型中参数β,回归函数g(·)和误差方差σ2的估计,并在适当条件下证明了估计量的强相合性。     

误差为线性过程时非参数回归模型变点的两步估计

本文给出误差为线性过程时非参数回归模型变点两步估计.第一步,给出变点位置的初始估计,并且证明了该估计量的相合性;第二步,在变点初始估计值的基础上推导出变点位置的最终估计量并给出了该估计量的收敛速度.数值模拟以及尼罗河数据实例分析的结果说明方法的有效性.     

一般增长曲线模型中随机回归系数线性估计的可容许性

本文在矩阵损失下研究了一般增长曲线模型中随机回归系数线性估计的可容许性。分别在齐次线性估计类和非齐次线性估计类中得到了随机回归系数的一个线性估计是可容许的充要条件。     

Proceedings of the Computer Science and Statistics: 12th Annual Symposium on the Interface

This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.     

Variance estimation for semiparametric regression models by local averaging

Variance estimation is a fundamental problem in statistical modelling and plays an important role in the inferences after model selection and estimation. In this paper, we focus on several nonparametric and semiparametric models and propose a local averaging method for variance estimation based on the concept of partial consistency. The proposed method has the advantages of avoiding the estimation of the nonparametric function and reducing the computational cost and can be easily extended to more complex settings. Asymptotic normality is established for the proposed local averaging estimators. Numerical simulations and a real data analysis are presented to illustrate the finite sample performance of the proposed method.     

Nonparametric estimation of mean and dispersion functions in extended generalized linear models

We study joint nonparametric estimators of the mean and the dispersion functions in extended double exponential family models. The starting point is the exponential family and the generalized linear models setting. The extended models allow for both overdispersion and underdispersion, or even a combination of both. We simultaneously estimate the dispersion function and the mean function by using P-splines with a difference type of penalty to avoid overfitting. Special attention is given to the smoothing parameter selection as well as to implementation issues. The performance of the method is investigated via simulations. A comparison with other available methods is made. We provide applications to several sets of data, including continuous data, counts and proportions.     

Wavelet penalized likelihood estimation in generalized functional models

The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in a functional influence of some covariates, we authorize others to be modeled linearly. We thus consider a generalized partially linear regression model with unknown regression coefficients and an unknown nonparametric function. We present a maximum penalized likelihood procedure to estimate the components of the model introducing penalty based wavelet estimators. Asymptotic rates of the estimates of both the parametric and the nonparametric part of the model are given and quasi-minimax optimality is obtained under usual conditions in literature. We establish in particular that the ? ¹-penalty leads to an adaptive estimation with respect to the regularity of the estimated function. An algorithm based on backfitting and Fisher-scoring is also proposed for implementation. Simulations are used to illustrate the finite sample behavior, including a comparison with kernel- and spline-based methods.     

Local polynomial regression smoothers with AR-error structure

Consider the fixed regression model with random observation error that follows an AR(1) correlation structure. In this paper, we study the nonparametric estimation of the regression function and its derivatives using a modified version of estimators obtained by weighted local polynomial fitting. The asymptotic properties of the proposed estimators are studied: expressions for the bias and the variance/covariance matrix of the estimators are obtained and the joint asymptotic normality is established. In a simulation study, a better behavior of the Mean Integrated Squared Error of the proposed regression estimator with respect to that of the classical local polynomial estimator is observed when the correlation of the observations is large. This work has been partially supported by grants PB98-0182-C02-01, PGIDT01PXI10505PR and MCyT Grant BFM2002-00265 (European FEDER support included).     

Bayes Linear Estimators

A class of linear estimators, called Bayes linear estimators, is developed by finding, among all linear estimators, ones which have least average total mean squared error, averaged over parameter points. Ridge, generalized ridge, restricted least squares, subset least squares, least squares, best, and generalized inverse linear estimators are all either Bayes linear estimators or limits of Bayes linear estimators. Results on Bayes linear estimators are extended to affine estimators. “Bootstrapping” procedures, in which the data are recycled in the guise of prior information, are discussed.     

Nonparametric density estimation in presence of bias and censoring

We consider projection estimator methods for the nonparametric estimation of the density of i.i.d. biased observations with a general known bias function w and under right censoring. Adaptive procedures to catch the optimal estimator among a collection by contrast penalization are investigated and proved to give efficient estimators with optimal nonparametric rates of convergence. Monte-Carlo experiments complete the study and illustrate the method.