删失数据下的变系数回归模型

研究了删失数据下的变系数回归模型．通过数据变换,利用局部多项式方法,给出了系数函数的局部加权最小二乘估计．证明了该估计的渐近偏差和渐近方差,同时获得了该估计的渐近正态性．     

IV模型中变点序贯检验方法

本文研究了IV模型中变点序贯检验问题.提出了基于加权残差部分和(weighted-CUSUM)的检验统计量.证明了其在原假设和备择假设下的极限性质.该检验方法在特征量与跃度非正交性条件下,当δ=1/2具有非平凡势,而当0≤δ<1/2时,则是相合的.     

Structural Change Models with an Application in Cryogenic Thermometry

In a linear regression framework, structural change models are proposed for the detection of abrupt changes in parameter values. Two models are discussed: 1) the pure structural change model, where all the components of the parameter are allowed to change and are tested all together, and 2) the partial structural change model, where only some of the parameter β components might change. For an on-line implementation, a sliding window algorithm is introduced. The procedure was successfully applied to phase transition identification in cryogenic thermometry. *Work partially funded under EU SofTools_MetroNet Contact N. G6RT-CT-2001-05061.     

Variography for Model Selection in Local Polynomial Regression with Spatial Data

In this work, we apply variographic techniques from spatial statistics to the problem of model selection in local polynomial regression with multivariate data. These techniques permit selection of the kernel and smoothing matrix with less computational load and interpretation of the regularity of the regression function in different directions. Moreover, they may represent the only feasible alternative for problems of a certain dimensionality.     

带有误差变量的自回归模型的局部多项式估计

该文主要研究带有误差变量的自回归模型的自回归函数的非参数估计问题,应用卷积核函数,给出了自回归函数的局部多项式估计,考察了局部多项式估计的相合性和渐近正态性,最后作了模拟计算.     

Recursive Estimation of Regression Functions by Local Polynomial Fitting

The recursive estimation of the regression function m(x) = E(Y/X = x) and its derivatives is studied under dependence conditions. The examined method of nonparametric estimation is a recursive version of the estimator based on locally weighted polynomial fitting, that in recent articles has proved to be an attractive technique and has advantages over other popular estimation techniques. For strongly mixing processes, expressions for the bias and variance of these estimators are given and asymptotic normality is established. Finally, a simulation study illustrates the proposed estimation method.     

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.     

时间序列中方差的结构变点的小波识别(英文)

本文给出了时间序列中方差的小波系数的两种估计:连续估计和离散估计.这两种估计可以用来检测时间序列中方差的结构变点.利用这两种估计我们给出了方差变点的位置和跳跃幅度的估计,并且显示出这些估计可达到最佳收敛速度.同时,我们还给出了这些估计的收敛速度以及检验统计量的渐进分布!     

Data Adaptive Ridging in Local Polynomial Regression

Abstract

When estimating a regression function or its derivatives, local polynomials are an attractive choice due to their flexibility and asymptotic performance. Seifert and Gasser proposed ridging of local polynomials to overcome problems with variance for random design while retaining their advantages. In this article we present a data-independent rule of thumb and a data-adaptive spatial choice of the ridge parameter in local linear regression. In a framework of penalized local least squares regression, the methods are generalized to higher order polynomials, to estimation of derivatives, and to multivariate designs. The main message is that ridging is a powerful tool for improving the performance of local polynomials. A rule of thumb offers drastic improvements; data-adaptive ridging brings further but modest gains in mean square error.     

Fixed Points in Tense Models

We study into definability of least fixed points in tense logic. It is proved that least fixed points of tense positive -operators are definable in transitive linear models. Examples are furnished showing that the least fixed points of tense positive operators may fail to be definable in the class of finite linearly ordered models, and the class of finite strictly linearly ordered models. Moreover, in dealing with the modal case, we point out examples of the non-definable inflationary points in the model classes mentioned.     

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This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method.     

Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation

Consider the polynomial regression model , where σ²(X)=Var(Y|X) is unknown, and ε is independent of X and has zero mean. Suppose that Y is subject to random right censoring. A new estimation procedure for the parameters β₀,...,β _p is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the method of Buckley and James (1979, Biometrika, 66, 429–436), but is, unlike the latter method, a noniterative procedure due to nonparametric preliminary estimation of the conditional regression function. The asymptotic normality of the estimators is established. Simulations are carried out for both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than the Buckley–James estimators. The two estimation procedures are also applied to a medical and an astronomical data set.     

Discriminant Analysis for Regression Models with Stationary Long-Memory Disturbances

We shall consider the problems of classifying an observation from regression model with stationary long-memory or short-memory disturbances into one of two populations described by the mean functions of the model. We use the log-likelihood ratio as a discrimant statistic which is optimal in the sense of its minimizing the misclassification probabilities. Then we confirm the theoretical results by some simple polynomial regression models.     

基于固定效应的纵向数据分位点回归模型的参数估计及CDM和MSOM的等价性

研究了基于固定效应的纵向数据模分位点回归模型的参数估计及统计诊断问题.首先给出了参数估计的MM迭代算法,然后讨论了统计诊断中数据删除模型(CDM)和均值移模型(MSOM)的等价性问题,最后利用消炎镇痛药数据说明了方法的应用.     

圆内亚纯函数与其微分多项式的公共Borel点

该文把A.P.Singh关于一类齐次微分多项式级的结果推广到更一般的微分多项式。并证明了：如果Q（f)≠0是圆内有限正级亚纯函数f的身长分多项式,则f^(k0Q(f)的Borel点必是f的Borel点,其中K0满足0≤K0≤min{K:f^(k)出现在Q（f)中}。     

缺失数据下线性模型中回归参数的经验似然置信区域

在缺失样本下,构造了线性模型中参数的调整的经验似然置信域,数值模拟表明调整的经验似然置信域有较好的覆盖率和精度.     

具有不同光滑变量的变系数模型

本文探讨具有不同光滑变量的变系数模型的建模、估计和估计的渐近性．首先,从实际出发建立模型;然后,使用局部线性方法给出模型中未知函数的初始估计,再使用平均方法,给出它们的平均估计;进—步,给出这些平均估计的渐近正态性．两个模拟例子说明这一估计方法是有效的．     

非线性回归校正模型在突变负荷预测中的研究及应用

非线性回归模型是中长期负荷预测的一种有效的方法,对常规变化趋势的负荷有很好的拟合性,但对有转折点的突变趋势或增长处于饱和阶段的负荷进行预测误差较大.通过对历史数据的最优分段,提出了非线性回归校正模型,可以很好地解决这个问题.实例表明,此模型在中长期负荷预测中是适用的,尤其对于有转折点的突变趋势,具有很高的预测精度.     

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??n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.     

Composite Quantile Regression for Functional Linear Models with Dependent Errors

n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.