变系数模型小波估计的渐近性

变系数模型是线性模型的有用推广,它允许回归系数是某个变量的函数,近年来在统计分析中得到广泛的应用.文中研究回归变量都是随机时的变系数模型,提出运用小波的方法估计变系数模型中的函数系数,并在较弱的条件下得到了变系数模型小波估计的渐近正态性.     

纵向数据变系数模型中的减元估计法

纵向数据变系数模型常应用于传染病学、生物医学和环境科学等领域. 本文提出了一种称为减元估计法的方法来估计模型中的未知函数和它们的导数. 减元估计法既适用于系数函数具有相同光滑度的情形, 也适用于系数函数具有不同光滑度的情形; 既适用于变量不依赖于时间的情形, 也适用于变量依赖于时间的情形. 给出了一般条件下估计量的局部渐近偏差、方差和渐近正态性, 并且渐近性结果显示: 当系数函数具有不同的光滑度时, 减元估计量的渐近方差比现有方法得到的估计量的渐近方差要少. 本文还通过 Monte Carlo 模拟研究了估计量的有限样本性质.     

删失数据下半变系数模型估计的渐近正态性

半变系数回归模型是变系数回归模型的有效推广,已获得了广泛的应用. 本文在响应变量随机删失下对其进行讨论,给出常系数和函数系数的估计, 并证明了该估计的渐近正态性.     

具有相关误差和不同光滑变量的半变系数模型估计（英文）

本文主要讨论具有相关误差和不同光滑变量的半变系数模型估计.通过改进的PLS估计,给出系数函数和常系数的估计,证明估计的渐近正态性,模拟研究说明了该估计的有效性.     

变系数混合模型的光滑样条推断

为了拟合纵向数据和其他相关数据,本文提出了变系数混合效应模型(VCMM).该模型运用变系数线性部分来表示协变量对响应变量的影响,而用随机效应来描述纵向数据组内的相关性, 因此,该模型允许协变量和响应变量之间存在十分灵活的泛函关系.文中运用光滑样条来估计均值部分的系数函数,而用限制最大似然的方法同时估计出光滑参数和方差成分,我们还得到了所提估计的计算方法.大量的模拟研究表明对于具有各种协方差结构的变系数混合效应模型,运用本文所提出的方法都能够十分有效地估计出模型中的系数函数和方差成分.     

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.     

变系数模型的小波估计

变系数模型是近年来文献中经常出现的一种统计模型.本文主要研究了变系数模型的估计问题,提出运用小波的方法估计变系数模型中的系数函数,小波估计的优点是避免了象核估计、光滑样条等传统的变系数模型估计方法对系数函数光滑性的一些严格限制. 并且,我们还得到了小波估计的收敛速度和渐近正态性.模拟研究表明变系数模型的小波估计有很好的估计效果.     

带约束条件的AGARCH模型

自Engle(1982）首创ARCH模型以来,各种推广和变异模型纷纷问世,形成庞大的ARCH类模型族。这些模型普遍存在一个缺陷：通常只限制条件方差的函数的系数非负以保证条件方差非负,并且在正态分布假设下用最大似然方法进行估计。本文明确提出带约束条件的AGARCH模型这一新概念,并用非线性规划方法代替最大似然方法对模型进行估计,实证结果表明这样的作法是可行且较优的。     

变系数的周期性时间序列模型及其应用

存在于各个领域的时间序列不仅表现出周期性的特征还易受外界因素的影响,而且外界因素的影响并非一成不变,同时,部分时间序列的周期是未知的.对于这样的易受外界因素影响的周期性时间序列,本文旨在构造含有变系数函数的周期性序列模型.将经典的时间序列模型分解成一个含有未知参数的部分线性变系数模型,利用B样条逼近外生变量的变系数函数,借助带有l₀惩罚项的最小二乘回归得到未知周期、周期序列以及外生变量的影响系数的估计结果.本文还给出了估计量的理论性质,包括周期估计的相合性、周期序列估计和变系数函数估计的渐近性质.通过第4章的模拟,我们展现了本文方法的优越性.最后我们通过三个实际数据的应用展现了本文方法的实用性.     

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．     

Statistical inference in partially-varying-coefficient single-index model

Consider a varying-coefficient single-index model which consists of two parts: the linear part with varying coefficients and the nonlinear part with a single-index structure, and are hence termed as varying-coefficient single-index models. This model includes many important regression models such as single-index models, partially linear single-index models, varying-coefficient model and varying-coefficient partially linear models as special examples. In this paper, we mainly study estimating problems of the varying-coefficient vector, the nonparametric link function and the unknown parametric vector describing the single-index in the model. A stepwise approach is developed to obtain asymptotic normality estimators of the varying-coefficient vector and the parametric vector, and estimators of the nonparametric link function with a convergence rate. The consistent estimator of the structural error variance is also obtained. In addition, asymptotic pointwise confidence intervals and confidence regions are constructed for the varying coefficients and the parametric vector. The bandwidth selection problem is also considered. A simulation study is conducted to evaluate the proposed methods, and real data analysis is also used to illustrate our methods.     

基于纵向数据的半参数变系数部分线性回归模型

纵向数据是数理统计研究中的复杂数据类型之一0,在生物、医学和经济学中具有广泛的应用．在实际中经常需要对纵向数据进行统计分析和建模．文章讨论了纵向数据下的半参数变系数部分线性回归模型,这里的纵向数据的在纵向观察在时间上可以是不均等的,也可看成是按某一随机过程来发生．所研究的半参数变系数模型包括了许多半参数模型,比如部分线性模型和变系数模型等．利用计数过程理论和局部线性回归方法,对于纵向数据下半参数变系数进行了统计推断,给出了参数分量和非参数分量的profile最小二乘估计,研究了这些估计的渐近性质,获得这些估计的相合性和渐近正态性．     

Varying-coefficient model for the occurrence rate function of recurrent events

This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences (ALIVE) cohort study.     

Testing hypotheses on the “drift” of parameters in ARMA and ARCH models

For an ARMA model, we test the hypothesis that the coefficients of this model remain constant in time and satisfy the stationarity condition against the alternative that the coefficients change (“drift”) in time. We propose asymptotically distribution free tests for such hypothesis based on sequential residual processes. A similar problem is solved for the ARCH model.      

Value at risk calculation through ARCH factor methodology: Proposal and comparative analysis

In this paper we put forward a new method to estimate value at risk (VaR), autoregressive conditional heteroskedastic (ARCH) factor, which combines multivariate analysis with ARCH models. Firstly, from a set of correlated portfolio risk factors, we derive a smaller uncorrelated risk factors set, by applying multivariate analysis. Secondly, we use ARCH schemes to model uncorrelated factors historical behaviour. Thirdly, we use the estimated models to predict future values for factors standard deviation. From them, VaR calculation is immediate. In this way, ARCH factor methodology overcomes the multivariate ARCH models drawbacks, which, in practice, make these unworkable for VaR calculation purposes. We apply the proposed methodology over a set of foreign exchange risk exposed portfolios, obtaining better results than those reached when J.P. Morgan’s Riskmetrics is used.     

Identification of Non-Varying Coefficients in Varying- Coefficient Models

A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F-approximation and three-moment X~2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory.     

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ( ).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.     

ARCH族模型及其对深圳股票市场的实证分析

ARCH族模型是动态非线性的股票定价模型,它在金融和经济领域具有广阔的应用前景.在短短二十年时间里取得了迅速的发展,先后提出了GARCH、ARCH-M、TARCH、EGRACH等模型丰富了ARCH族模型.本文从ARCH族模型出发,简要介绍了其主要形式和特点,然后将ARCH族模型运用于我国深圳股票市场的实证分析,从实证结果中总结深圳股市的总体特征.     

Efficient estimation of a varying-coefficient partially linear binary regression model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.