核实数据下非线性半参数EV模型的经验似然推断

考虑带有协变量误差的非线性半参数模型,借助于核实数据,本文构造了未知参数的三种经验对数似然比统计量,证明了所提出的统计量具有渐近X2分布,此结果可以用来构造未知参数的置信域．另外,本文也构造了未知参数的最小二乘估计量,并证明了它的渐近性质．仅就置信域及其覆盖概率的大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣．     

Estimating Functions for Nonlinear Time Series Models

This paper discusses the problem of estimation for two classes of nonlinear models, namely random coefficient autoregressive (RCA) and autoregressive conditional heteroskedasticity (ARCH) models. For the RCA model, first assuming that the nuisance parameters are known we construct an estimator for parameters of interest based on Godambe's asymptotically optimal estimating function. Then, using the conditional least squares (CLS) estimator given by Tjøstheim (1986, Stochastic Process. Appl., 21, 251–273) and classical moment estimators for the nuisance parameters, we propose an estimated version of this estimator. These results are extended to the case of vector parameter. Next, we turn to discuss the problem of estimating the ARCH model with unknown parameter vector. We construct an estimator for parameters of interest based on Godambe's optimal estimator allowing that a part of the estimator depends on unknown parameters. Then, substituting the CLS estimators for the unknown parameters, the estimated version is proposed. Comparisons between the CLS and estimated optimal estimator of the RCA model and between the CLS and estimated version of the ARCH model are given via simulation studies.     

Outlier Detections in Autoregressive Models

This article proposes a new technique for detecting outliers in autoregressive models and identifying the type as either innovation or additive. This technique can be used without knowledge of the true model order, outlier location, or outlier type. Specifically, we perturb an observation to obtain the perturbation size that minimizes the resulting residual sum of squares (SSE). The reduction in the SSE yields outlier detection and identification measures. In addition, the perturbation size can be used to gauge the magnitude of the outlier. Monte Carlo studies and empirical examples are presented to illustrate the performance of the proposed method as well as the impact of outliers on model selection and parameter estimation. We also obtain robust estimators and model selection criteria, which are shown in simulation studies to perform well when large outliers occur.     

非线性回归模型的经验似然诊断

经验似然方法已经被广泛用于线性模型和广义线性模型.本文基于经验似然方法对非线性回归模型进行统计诊断.首先得到模型参数的极大经验似然估计;其次基于经验似然研究了三种不同的影响曲率度量;最后通过一个实际例子,说明了诊断方法的有效性.     

杂草种子运动的矩阵模型

人类活动(如耕作等)、捕食者活动(如蚂蚁、蚯蚓等)及一些无生命因素(如下雨、冰雪覆盖等),使土壤中的杂草种子在土壤中各个方向上不断运动,运用L eslie矩阵和M arkov链建立了一个具年龄结构的杂草种子在土壤中随时间动态变化的一般矩阵模型.     

Estimating the Density of the Residuals in Autoregressive Models

We consider a (nonlinear) autoregressive model with unknown parameters (vector θ). The aim is to estimate the density of the residuals by a kernel estimator. Since the residuals are not observed, the usual procedure for estimating the density of the residuals is the following: first, compute an estimator for θ; second, calculate the residuals by use of the estimated model; and third, calculate the kernel density estimator by use of these residuals. We show that the resulting density estimator is strong consistent at the best possible convergence rate. Moreover, we prove asymptotic normality of the estimator. This revised version was published online in June 2006 with corrections to the Cover Date.     

Statistical Inference in Single-Index and Partially Nonlinear Models

A finite series approximation technique is introduced. We first applythis approximation technique to a semiparametric single-index model toconstruct a nonlinear least squares (LS) estimator for an unknown parameterand then discuss the confidence region for this parameter based on theasymptotic distribution of the nonlinear LS estimator. Meanwhile, acomputational algorithm and a small sample study for this nonlinear LSestimator are developed. Additionally, we apply the finite seriesapproximation technique to a partially nonlinear model and obtain some newresults.     

Estimating Mixture of Dirichlet Process Models

Abstract

Current Gibbs sampling schemes in mixture of Dirichlet process (MDP) models are restricted to using “conjugate” base measures that allow analytic evaluation of the transition probabilities when resampling configurations, or alternatively need to rely on approximate numeric evaluations of some transition probabilities. Implementation of Gibbs sampling in more general MDP models is an open and important problem because most applications call for the use of nonconjugate base measures. In this article we propose a conceptual framework for computational strategies. This framework provides a perspective on current methods, facilitates comparisons between them, and leads to several new methods that expand the scope of MDP models to nonconjugate situations. We discuss one in detail. The basic strategy is based on expanding the parameter vector, and is applicable for MDP models with arbitrary base measure and likelihood. Strategies are also presented for the important class of normal-normal MDP models and for problems with fixed or few hyperparameters. The proposed algorithms are easily implemented and illustrated with an application.     

基于MCMC算法的贝叶斯变结构分位自回归模型研究

为了更全面细致的刻画时间序列变结构性的特征及其相依性,提出了一类马尔可夫变结构分位自回归模型。利用非对称Laplace分布构建了模型的似然函数,证明了当回归系数的先验分布选择为扩散先验分布时,参数的各阶后验矩都是存在的,并给出了能确定变点位置和性质的隐含变量的后验完全条件分布。仿真分析结果发现马尔可夫变结构分位自回归模型可以全面有效地实现对时间序列数据变结构性的刻画。并应用贝叶斯Markov分位自回归方法分析了中国证券市场的变结构性,结果发现中国证券市场在不同阶段尾部表现出不同的相依性。     

Estimating Joint Distributions of Markov Chains

Suppose we observe a stationary Markov chain with unknown transition distribution. The empirical estimator for the expectation of a function of two successive observations is known to be efficient. For reversible Markov chains, an appropriate symmetrization is efficient. For functions of more than two arguments, these estimators cease to be efficient. We determine the influence function of efficient estimators of expectations of functions of several observations, both for completely unknown and for reversible Markov chains. We construct simple efficient estimators in both cases.     

General Autoregressive Models with Long-Memory Noise

We give the limiting distribution of the least-squares estimator in the general autoregressive model driven by a long-memory process. We prove that with an appropriate normalization the estimation error converges, in distribution, to a random vector which contains: (1) a stochastic component, due to the presence of the unstable roots, which are multiple Wiener–Itô integrals and a non-linear functionals of stochastic integrals with respect to a Brownian motion; (2) a constant component due to the stable roots; (3) a stochastic component, due to the presence of the explosive roots, which is a mixture of normal distributions.     

Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate nonparametrically some characteristics of this conditional distribution. Kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density are introduced. Asymptotic properties are stated for each of these estimates, and they are applied to the estimations of the conditional mode and conditional quantiles. Our asymptotic results highlightes the importance of the concentration properties on small balls of the probability measure of the underlying functional variable. So, a special section is devoted to show how our results behave in several situations when the functional variable is a continuous time process, with special attention to diffusion processes and Gaussian processes. Even if the main purpose of our paper is theoretical, an application to some chemiometrical data set coming from food industry is presented in a short final section. This example illustrates the easy implementation of our method as well as its good behaviour for finite sample sizes.     

通用系统模糊可靠度计算模型

对系统组成单元的含义作了新的定义,建立了单元模糊可靠度及其置信区间的估计模型;建立了常见通用系统的模糊可靠度估计模型;通过对单元模糊可靠度的直接估计,利用所建立的估计模型可以快速方便地预测出系统的模糊可靠度.实例分析给出了估计模型的使用方法,并显示了模型的有效性.     

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21].     

广义Pareto分布参数的经验Bayes估计的收敛速度

在加权平方损失函数下,获得广义Pareto分布形状参数的经验Bayes(EB)估计,并得到了该估计的收敛速度.     

函数系数线性自回归模型的样条估计

基于多项式样条全局光滑方法,建立函数系数线性自回归模型中系数函数的样条估计.在适当条件下,证明了系数函数多项式样条估计的相合性,并给出了它们的收敛速度.模拟例子验证了理论结果的正确性.     

基于残差加权经验过程方法的自回归模型分布变点监测

Change monitoring of distribution in time series models is an important issue.This paper proposes a procedure for monitoring changes in the error distribution of autoregressive time series,which is based on a weighed empirical process of residuals with weights equal to the regressors.The asymptotic properties of our monitoring statistic are derived under the null hypothesis of no change in distribution.The finite sample properties are investigated by a simulation.As it turns out,the procedure is not only able to detect distributional changes but also changes in the regression coefficient and mean.Finally,we apply the statistic to a groups of financial data.     

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.     

非线性半参数回归模型中参数的经验似然置信域

该文考虑非线性半参数回归模型,构造了模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近Χ²分布,由此结果可以用来构造未知参数的置信域.另外,该文也构造了未知参数 的最小二乘估计量,并证明了它的渐近性质.仅就置信域精度及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣.     

重尾非线性自回归模型自加权M-估计的渐近分布

考虑非线性自回归模型x_t=f(x_t-1,…,x_t-p,θ)+∈_t,其中θ为q维未知参数,{∈_t}为随机误差.在允许误差方差无穷的重尾条件下,构造θ的自加权M-估计,并证明了该估计的渐近正态性.最后通过数值模拟,在随机误差服从某些重尾分布的条件下,说明自加权M-估计比最小二乘和L₁估计更有效.