ρ-混合序列加权和的完全收敛性及其应用

本文研究了ρ-混合序列加权和的一些强极限定理,利用最大值矩不等式,获得了ρ-混合序列加权和的完全收敛性.并将此结果应用于线性回归模型参数的最小二乘估计及非参数回归模型的权函数估计.     

误差为NSD序列的广义线性模型的M估计的强相合性

研究了以NSD序列(negatively superadditive dependent)为误差的广义线性模型,得到了未知参数的M估计.在较弱的条件下,利用指数不等式、NSD序列加权和的强收敛性和Borel-Cantelli引理等证明了未知参数M估计的强相合性.此结果推广了独立误差和NSD误差的线性模型的相应结果.     

强混合序列的一类中心极限定理及其在回归模型中的应用[英文]

本文研究了强混合序列加权和的中心极限定理, 同时也给出了强混合序列线性过程部分和的中心极限定理. 作为应用,我们利用所得结果, 证明了固定设计回归模型中一类加权函数估计的渐近正态性.     

强混合序列的一类中心极限定理及其在回归模型中的应用(英文)

本文研究强混合序列加权和的中心极限定理,同时也给出强混合序列线性过程部分和的中心极限定理.作为应用,利用所得结果,证明固定设计回归模型中一类加权函数估计的渐近正态性.     

多元非参数计量经济模型的变窗宽局部线性估计

在随机设计(模型中所有变量为随机变量)下,提出了非参数计量经济模型的变窗宽局部线性估计,并利用概率论中大数定理和中心极限定理,在内点处证明了它的一致性和渐近正态性.它在内点处的收敛速度达到了非参数函数估计的最优收敛速度.     

随机适应误差下线性模型参数M估计的渐近性质

在一些较弱的充分条件下,本文研究了误差为随机适应序列下,线性模型回归参数M估计的强相合性.与文献中已有结果比较,扩大了应用范围,且对矩条件也有较大改进.同时我们给出了随机适应误差下线性模型参数M估计的渐近正态性.     

一类线性混合模型的谱分解估计

谱分解估计(SDE)是新近提出的关于线性混合模型参数的一种新的估计方法,此方法的一个突出特点是同时给出固定效应参数和方差分量的显式解估计．本文就含两个方差分量的线性混合模型,对谱分解估计的性质做了进一步的研究,获得了方差分量的SDE和方差分析估计相等的充分必要条件,证明了在一定的条件下方差分量的SDE为一致最小方差无偏估计．     

非参数计量经济联立模型的局部线性两阶段最小二乘变窗宽估计

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用 .本文在随机设计 (模型中所有变量为随机变量 )下 ,提出了非参数计量经济联立模型的局部线性两阶段最小二乘变窗宽估计并利用概率论中大数定理和中心极限定理在内点处研究了它的大样本性质 ,证明了它的一致性和渐近正态性 .它在内点处的收敛速度达到了非参数函数估计的最优收敛速度 .     

混合线性模型M估计的强相合性

研究了混合样本线性模型中回归参数M估计的强相合性,在较弱的矩条件下,获得了M估计是强相合的充分条件,实质性地改进和推广了文[1]定理3.1.     

凸约束广义线性回归模型的参数估计及算法

本文将从实际评估工作中提练出来的一种评估模型推广至因变量未知且带有一般性凸约束条件的广义线性模型,证明了模型解的存在唯一性,并从解的几何背景出发,提出了基于凸集间交互投影的参数最小二乘估计的有效算法.结合模型的特点,引入EM算法给出了参数的极大似然估计.模型的提出丰富了线性模型的结构框架,算法的给出为参数估计提供了行之有效的计算方法.     

Bayesian Monte Carlo estimation for profile hidden Markov models

Hidden Markov models are used as tools for pattern recognition in a number of areas, ranging from speech processing to biological sequence analysis. Profile hidden Markov models represent a class of so-called “left–right” models that have an architecture that is specifically relevant to classification of proteins into structural families based on their amino acid sequences. Standard learning methods for such models employ a variety of heuristics applied to the expectation-maximization implementation of the maximum likelihood estimation procedure in order to find the global maximum of the likelihood function. Here, we compare maximum likelihood estimation to fully Bayesian estimation of parameters for profile hidden Markov models with a small number of parameters. We find that, relative to maximum likelihood methods, Bayesian methods assign higher scores to data sequences that are distantly related to the pattern consensus, show better performance in classifying these sequences correctly, and continue to perform robustly with regard to misspecification of the number of model parameters. Though our study is limited in scope, we expect our results to remain relevant for models with a large number of parameters and other types of left–right hidden Markov models.     

右删失时间序列AR模型参数估计

通过Kaplan-Meier估计和Nelson-Aalen估计得到了平稳时间序列被另一平稳序列右删失下.AR模型的参数估计.首先,通过与完全数据下的参数估计进行对比,说明了两种估计方法的效果.然后,根据计算机模拟的样本量以及删失率的不同,对比了两种估计的优劣,并且模拟结果表明两种估计是有效的.     

A multivariate Markov chain model for categorical data sequences and its applications in demand predictions

Markov models are commonly used in modelling many practicalsystems such as telecommunication systems, manufacturing systemsand inventory systems. In this paper we propose a multivariateMarkov chain model for modelling multiple categorical data sequences.We develop efficient estimation methods for the model parameters.We then apply the model and method to demand predictions fora soft-drink company in Hong Kong.     

Improved probabilistic point estimation schemes for uncertainty analysis

The probabilistic point estimation (PPE) methods replace the probability distribution of the random parameters of a model with a finite number of discrete points in sample space selected in such a way to preserve limit probabilistic information of involved random parameters. Most PPE methods developed thus far match the distribution of random parameters up to the third statistical moment and, in general, could provide reasonable accurate estimation only for the first two statistical moments of model output. This study proposes two optimization-based point selection schemes for the PPE methods to enhance the accuracy of higher-order statistical moments estimation for model output. Several test models of varying degrees of complexity and nonlinearity are used to examine the performance of the proposed point selection schemes. The results indicate that the proposed point selection schemes provide significantly more accurate estimation of model output uncertainty features than the existing schemes.     

Estimation with Missing Data

This paper reviews estimation problems with missing, or hidden data. We formulate this problem in the context of Markov models and consider two interrelated issues, namely, the estimation of a state given measured data and model parameters, and the estimation of model parameters given the measured data alone. We also consider situations where the measured data is, itself, incomplete in some sense. We deal with various combinations of discrete and continuous states and observations.     

Estimation in the presence of many nuisance parameters: Composite likelihood and plug-in likelihood

We consider the incidental parameters problem in this paper, i.e. the estimation for a small number of parameters of interest in the presence of a large number of nuisance parameters. By assuming that the observations are taken from a multiple strictly stationary process, the two estimation methods, namely the maximum composite quasi-likelihood estimation (MCQLE) and the maximum plug-in quasi-likelihood estimation (MPQLE) are considered. For the MCQLE, we profile out nuisance parameters based on lower-dimensional marginal likelihoods, while the MPQLE is based on some initial estimators for nuisance parameters. The asymptotic normality for both the MCQLE and the MPQLE is established under the assumption that the number of nuisance parameters and the number of observations go to infinity together, and both the estimators for the parameters of interest enjoy the standard root-n$n$ convergence rate. Simulation with a spatial–temporal model illustrates the finite sample properties of the two estimation methods.     

On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs

A space-time random set is defined and methods of its parameters estimation are investigated. The evolution in discrete time is described by a state-space model. The observed output is a planar union of interacting discs given by a probability density with respect to a reference Poisson process of discs. The state vector is to be estimated together with auxiliary parameters of transitions caused by a random walk. Three methods of parameters estimation are involved, first of which is the maximum likelihood estimation (MLE) for individual outputs at fixed times. In the space-time model the state vector can be estimated by the particle filter (PF), where MLE serves to the estimation of auxiliary parameters. In the present paper the aim is to compare MLE and PF with particle Markov chain Monte Carlo (PMCMC). From the group of PMCMC methods we use specially the particle marginal Metropolis-Hastings (PMMH) algorithm which updates simultaneously the state vector and the auxiliary parameters. A simulation study is presented in which all estimators are compared by means of the integrated mean square error. New data are then simulated repeatedly from the model with parameters estimated by PMMH and the fit with the original model is quantified by means of the spherical contact distribution function.     

两步估计法在非等间距GM(1,1)预测模型参数估计中的应用

为提高灰色模型的预测精度,在传统建模基础上,通过分析模型解的结构,提出了一种新的方法一两步估计法.即第1步利用差分思想,给出参数的初始估计值;第2步采用非齐次指数函数优化背景值,结合积分理论,对初始估计进行修正.实例表明,方法不仅适用于非等间距模型,同样也适合等间距模型,并且模型精度理想.     

Estimation of elastic coefficients for a multiple beam structure

In this paper, we consider the estimation of spatially dependent elastic parameters in a static distributed model of a simple structure composed of two beams at a fixed angle to one another. We formulate the potential energy functional of the system and obtain existence of optimal estimators to a regularized-output least-squares estimation problem. We discuss regularity and approximation results for the basic problem and penalized problem in which nonconforming elements are used to model the junction of the beams. Numerical examples are presented and generalizations to multiple-beam systems are discussed.This work was supported in part by AFOSR Grant 91-0017.