NA序列半参数回归模型小波估计的强相合性

对于半参数回归模型yi=xiβ+g(ti)+ei,i=1,2,…,n,对误差{ei,1≤i≤n}为NA序列,在适当的条件下研究了未知参数β的小波估计的强相合,同时也得到了未知函数g(t)的小波估计的一致强相合.     

Asymptotics for Wavelet Based Estimates of Piecewise Smooth Regression for Stationary Time Series

Wavelet methods are used to estimate density and (auto-) regression functions that are possibly discontinuous. For stationary time series that satisfy appropriate mixing conditions, we derive mean integrated squared errors (MISEs) of wavelet-based estimators. In contrast to the case for kernel methods, the MISEs of wavelet-based estimators are not affected by the presence of discontinuities in the curves. Applications of this approach to problems of identification of nonlinear time series models are discussed.     

随机设计下非参数回归模型变点的小波检测与估计

A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.     

Nonparametric prediction of a Hilbert space valued random variable

Let $\text{ξ}{}_{\mathrm{t}}\text{, t ?}\text{R}$, be a Markovian, measurable, strictly stationary process taking values in a measurable space (E, $\text{B}$), and g a mapping from E into a separable Hilbert space H. A statistical nonparametric predictor of g(ξ_T+h) is studied in the paper. That predictor, based on the observations of the process between the times O and T generalizes the ‘predictogram’; its asymptotic consistency is proved and some applications are given.     

拟蒙特卡罗方法用于估计多元回归函数

拟蒙特卡罗（QMC）方法被广泛用于解决数值分析和统计学中的各种问题，比如数值积分，最优化，试验设计，随机过程的模拟等．本文研究该方法在估计多元回归函数中的应用．证明了，在相当一般的条件下，均匀设计（或者，“代表点设计”）与回归函数傅里叶系数的QMC估计（对应地，使用拟随机重要性抽样的QMC估计）一起，构成一个回归函数的渐近最优投影估计．     

变窗宽局部线性回归中的M估计

In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.     

投影寻踪回归在试验设计分析中的应用研究

本文对三个应用实例进行分析，研究结果表明：ＰＰＲ方法是试验设计回归分析行之有效的方法，它给技术工作者提供了一个处理试验数据的崭新统计方法。ＰＰＲ的应用，将会大幅度降低试验费用，提高试验研究工作效率。     

岭回归分析的SAS程序设计

田俊．岭回归分析的ＳＡＳ程序设计．岭回归分析方法是传统的多元回归分析方法的一个补充,在实际工作中经常使用。但是在标准统计软件ＳＡＳ中没有专门的岭回归分析过程,本文介绍如何通过设置伪样品后使用ＳＡＳ进行岭回归分析     

删失回归模型的随机加权逼近

Raoand Zhao(1992)提出了一种用随机加权的方法去逼近线性回归模型中M-估计的渐近分布。之前，Fang and zhao(2002)把这种方法推广到设计阵是随机的删失回归模型．本文，我们把这个结果推广到设计阵是非随机的删失回归模型，并证明该随机加权方法的一些大样本性质。     

一类非参数回归模型核估计的渐近性质

研究一类新的非参数回归模型回归函数的核估计问题,其中误差项为一阶非参数自回归方程.通过重复利用Watson-Nadaraya核估计方法,构造了回归函数及误差回归函数的估计量分别为m(.)和ρ(.),在适当的条件下,证明了估计量m(.)和ρ(.)的渐近正态性.     

非参数回归函数的稳健Bootstrap

在有异常值的数据中,Bootstrap样本可能比原有样本含有更高的“污染”,这会降低所要做的统计推断的有效性.本文讨论在非参数回归N-W估计中,如何利用影响函数得到重新抽样的概率,使用倾斜的Bootstrap方法得到曲线的拟合,从而达到有效地抵制异常值对回归函数影响的目的,数值模拟的结果表明这种处理方式的有效性.     

Design Adaptive Nearest Neighbor Regression Estimation

This paper deals with nonparametric regression estimation under arbitrary sampling with an unknown distribution. The effect of the distribution of the design, which is a nuisance parameter, can be eliminated by conditioning. An upper bound for the conditional mean squared error of k−NN estimates leads us to consider an optimal number of neighbors, which is a random function of the sampling. The corresponding estimate can be used for nonasymptotic inference and is also consistent under a minimal recurrence condition. Some deterministic equivalents are found for the random rate of convergence of this optimal estimate, for deterministic and random designs with vanishing or diverging densities. The proposed estimate is rate optimal for standard designs.     

经典的用回归模型进行统计控制中的问题

利用回归模型进行统计控制,在实际工作中一直得到广泛应用。通常采用的方法是利用回归模型y^=a+bx进行逆估计,即根据回归模型的变换x=(y^-a)/b,由应变量Y的取值范围反推自变量X的取值范围。本文指出这种方法是很不合理的;进一步提出二种相对合理取代的统计方法。     

On Confidence Intervals in Nonparametric Binary Regression via Edgeworth Expansions

Local confidence intervals for regression function with binary response variable are constructed. These intervals are based on both theoretical and “plug-in” normal asymptotic distribution of a usual statistic. In the plug-in approach, two ways of estimating bias are proposed; for them we obtain the mean squared error and deduce an expression of an optimal bandwidth. The rate of convergence of theoretical distributions to their limits is obtained by means of Edgeworth expansions. Likewise, these expansions allow us to deduce properties about the coverage probability of the confidence intervals. Theoretic approximations to that probability are compared in a simulation study with the corresponding coverage rates.     

基于半参数分位数回归的居民个人收入研究

教育、性别、年龄、城乡、地区经济都是影响居民个人收入的重要因素,这些因素影响收入的作用方式是不同的,有的以参数形式存在,有的则是非参数形式存在.同时,这些因素在收入的不同分位点影响收入的程度也是不同的,通过构造半参数分位数回归模型,对影响收入诸因素的作用方式与程度进行了研究.     

非参数回归函数之改良基于分割的估计的强相合性（英）

设(X,Y),(X1,Y1),…,(XnYn)为取值于 Rd× R的 i．i．d．随机变量,E(|Y|) ＜∞．设mn(x)为回归函数m(x)=E(|Y|X=x)基于分割的估计,本文在对mn(x)进行改良的条件下得到改良的基于分割的强相合估计．     

协整回归残量平稳性的小波检验

本文研究基于小波方法的协整回归残量平稳性检验。将文献[6]中的小波方法推广到了协整关系的检验,给出了对线性协整模型OLS回归后得到的残量进行平稳性检验的小波方法,得到了在原假设非协整下检验统计量的渐近分布。模拟实验和实例分析都验证了新方法的有效性。     

Estimation de la transition de probabilité d'une chaîne de Markov doëblin-récurrente. étude du cas du processus autorégressif général d'ordre 1

We consider an homogenous Markov chain {X_n}. We estimate its transition probability density with kernel estimators. We apply these methods to the estimation of the unknown function f of the process defined by X₁ and X_n+1 = f(X_n) + ε_n, where {ε_n} is a noise (sequence of independent identically distributed random variables) of unknown law. The mean quadratic integrated rates of convergence are identical to those of classical density estimations. These risks are used here because we want some global informations about our estimates. We also study the average of those risks when the variance changes; it is shown that they reach a minimal value for some optimal variance. We study uniform convergence of our estimators. We finally estimate the variance of the noise and its density.     

随机设计下非参数回归模型方差变点Ratio检验

研究随机设计下非参数回归模型方差变点Ratio检验.首先用局部多项式方法估计回归曲线得到残差序列,其次基于残差的平方序列构造Ratio检验统计量并推导检验统计量的极限分布.最后数值模拟与实例分析结果表明方法的有效性.     

Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression

We study Beran's extension of the Kaplan-Meier estimator for thesituation of right censored observations at fixed covariate values. Thisestimator for the conditional distribution function at a given value of thecovariate involves smoothing with Gasser-Müller weights. We establishan almost sure asymptotic representation which provides a key tool forobtaining central limit results. To avoid complicated estimation ofasymptotic bias and variance parameters, we propose a resampling methodwhich takes the covariate information into account. An asymptoticrepresentation for the bootstrapped estimator is proved and the strongconsistency of the bootstrap approximation to the conditional distributionfunction is obtained.