部分可观测信息条件下的视情维修模型参数估计

在部分可观测信息条件下,文章针对装备的性能退化信息不完备和历史寿命信息随机截尾问题,建立了装备故障率服从比例故障率模型(PHM)的视情维修模型,给出了表达观测值与退化状态之间随机关系的观测概率矩阵和表达装备退化状态之间随机关系的状态转移概率矩阵;推导出装备在随机截尾数据情况下的可靠度函数、故障率函数及其似然函数;并利用粒子群优化(PSO)算法解决了该模型的参数估计问题。通过仿真分析PSO算法对视情维修模型的极大似然估计(MLE),验证了该方法的收敛性和稳定性。     

基于优先度的概率区间型决策

对于不确定条件下决策问题的研究,自然状态发生概率的确定是其难点之一。文章阐述了自然状态发生的概率不能完全确定但可以估计其所在区间的决策问题及其性质,给出了决策方案效益期望值极值的算法和一种新的优先度的算法,最后给出了概率区间型决策问题基于优先度的决策方法。     

基于Bayesian Gibbs Sampler的状态空间模型估计方法研究及其在中国潜在产出估计上的应用

 本文将贝叶斯吉伯斯样本生成（Bayesian Gibbs Sampling，BGS）方法应用到状态空间模型的估计。首先介绍了BGS方法的基本内容和计算步骤，然后给定参数生成满足状态空间模型的模拟数据，并对模拟数据应用BGS方法估计。结果表明参数与状态向量的估计值与参数值与状态向量的真实值相当接近，明显优于基于Kalman滤波的最大似然估计结果。最后，本文将BGS算法应用于中国1980年至2008年的潜在增长率与增长率缺口的估计。     

关于部分可观测条件Gauss随机序列的最佳递推滤波估计

0 引言为了给信息管理自动化提供一种理想的数学处理手段,本文将应用滤波理论在研究一类条件Gauss有谱广义平稳随机序列最佳递推滤波估计的基础上,进一步论讨一类部分可观测“有用信号”在均方意义下的最佳线性递推估计与误差问题。讨论结果表明,本文得到的最佳递推滤波方程,对解决该类广义平稳随机序列的非观测分量依可观测分量的最佳估计效果甚佳。     

证券投资的一种预测方法

本文提出证券投资的一个预测方法--E Bayes方法,不仅能预测证券价格的走势,而且还能更进一步地指出证券价格的范围.本文以下首先把数据进行分组,给出预测对象的状态划分,然后在此基础上给出状态概率的E Bayes估计的定义和E Bayes估计,根据状态概率进行预测.     

基于卡尔曼滤波估计的连续性抽样调查研究

 针对连续性抽样调查中如何提高连续调查数据准确性的问题，本文引入时间序列分析方法，分别考虑连续性抽样调查中的重复样本和轮换样本等不同情况，建立了连续性抽样调查下的状态空间模型，利用成熟的卡尔曼滤波估计方法给出了总体均值的估计量。由于状态空间模型及卡尔曼滤波估计方法能够充分利用各期连续样本的调查信息，给出了精度更高的估计量，从而能够产生更加准确的连续性时间序列数据。     

时变参数状态空间模型估计研究

在宏观经济和金融资本市场上广泛存在着非线性时变参数时间序列,而当前的研究主要关注静态参数状态空间模型的估计。本文通过引入变点分析,改进了静态参数的粒子学习滤波技术,提出了变点粒子学习滤波技术,用于估计时变参数状态空间模型。并且利用模拟实验同经典的变结构IMM滤波技术进行了对比,结果显示,本文提出的变点粒子学习滤波在动态模拟样本数据方面具有更大的优势。可以用于对股票价格和成交量的联合动态轨迹进行实时的模拟追踪。     

不放回样本追加策略下域的估计

 本文研究了不放回追加策略，包括基本设计和域追加设计都为简单随机抽样、分层随机抽样情形下不放回样本追加时域的估计的问题。根据不同的抽样设计给出单元的一阶及二阶包含概率的具体计算公式，并构造总体总量和域总量的Horvitz—Thompson型估计，然后基于简单随机抽样的不放回追加抽样方案，给出总体单元的前两阶包含概率。及该方案在分层抽样下的推广，在有辅助信息可用时构造域总量的分层联合比估计，并给出其方差和方差估计公式，同时我们给出了模拟结果，从模拟结果可以看出，给出的方差估计是估计量方差的近似无偏估计。     

在非高斯状态空间模型下对SCD模型的估计

高频超高频时间序列的分析与建模成已为计量经济的一个全新研究领域,而研究金融市场中交易事件到达时间的随机条件持续期SCD模型,因为加入了随机变量,可以更好地拟合高频超高频金融时间序列特有的统计特征,但随机变量的引入给模型估计带来了估计困难。考虑到非高斯状态空间模型与随机条件持续期SCD模型各自的优势,文章将SCD模型转换成非高斯状态空间模型,从而利用非高斯状态空间框架下的Kalman滤波解决了SCD模型的估计难题。     

中国农村居民的健康动态研究

 利用四轮中国健康与营养状况调查构成的面板数据（1997-2006），本文研究了中国农村居民的健康动态决定过程及健康持续性。我们使用动态随机效应probit模型控制了个体的不可观测异质性。同时，为了避免状态依赖效应的估计偏差，本文分别采纳了Heckman(1981)和Wooldridge(2005)提出的估计方法来处理“初始条件问题”。结论表明：在控制了其他因素之后，状态依赖效应对中国农村居民健康状况具有显著的影响；此外，那些年龄较大、教育水平较低、收入水平较低的农村弱势群体陷入持续性健康问题的可能性更大。     

An EM-Based Viterbi Approximation Algorithm for Mixed-State Latent Factor Models

In this article, a state-space model based on an underlying hidden Markov chain model (HMM) with factor analysis observation process is introduced. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a conditionally heteroscedastic factor analysis observation process. More specifically, we concentrate on situations where the factor variances are modeled by univariate Generalized Quadratic Autoregressive Conditionally Heteroscedastic processes (GQARCH). An expectation maximization (EM) algorithm combined with a mixed-state version of the Viterbi algorithm is derived for maximum likelihood estimation. The various regimes, common factors, and their volatilities are supposed unobservable and the inference must be carried out from the observable process. Extensive Monte Carlo simulations show promising results of the algorithms, especially for segmentation and tracking tasks.     

Nonparametric Bayesian analysis for multi-site hidden Markov model

The hidden Markov model (HMM) provides an attractive framework for modeling long-term persistence in a variety of applications including pattern recognition. Unlike typical mixture models, hidden Markov states can represent the heterogeneity in data and it can be extended to a multivariate case using a hierarchical Bayesian approach. This article provides a nonparametric Bayesian modeling approach to the multi-site HMM by considering stick-breaking priors for each row of an infinite state transition matrix. This extension has many advantages over a parametric HMM. For example, it can provide more flexible information for identifying the structure of the HMM than parametric HMM analysis, such as the number of states in HMM. We exploit a simulation example and a real dataset to evaluate the proposed approach.     

Working life expectancies: the case of Finland 1980–2006

Summary.  Working life expectancy is the future time that a person is expected to spend in employment. The paper is concerned with its estimation jointly with the expected times spent in the related states of 'on disability pension' and 'other alive'. The method, which is novel in this field, first estimates year- and age-dependent probabilities of being in the states of interest by large sample multivariate logistic regression. Estimates of probabilities, and subsequently expectancies, are given for the case of Finnish women and men aged 16–64 years for selected years in the period 1980–2001, together with projections for 2006. Since 1996 the decline in the employment of males has largely been due to the increasing popularity of early retirement. It was not due to an increase in disability. There has been no such decline for women, and the working life expectancy for males has been predicted to decline to or to fall below the initially lower figure for females by 2006. Considering that the Finnish population is aging rapidly, these trends could entail serious social and economic consequences for society in the coming years because of a looming shortage in the labour force that could undermine the sustainability of a welfare state.     

ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

On the efficiency of nonparametric variance estimation in sequential dose-finding

Dose-finding in clinical studies is typically formulated as a quantile estimation problem, for which a correct specification of the variance function of the outcomes is important. This is especially true for sequential study where the variance assumption directly involves in the generation of the design points and hence sensitivity analysis may not be performed after the data are collected. In this light, there is a strong reason for avoiding parametric assumptions on the variance function, although this may incur efficiency loss. In this paper, we investigate how much information one may retrieve by making additional parametric assumptions on the variance in the context of a sequential least squares recursion. By asymptotic comparison, we demonstrate that assuming homoscedasticity achieves only a modest efficiency gain when compared to nonparametric variance estimation: when homoscedasticity in truth holds, the latter is at worst 88% as efficient as the former in the limiting case, and often achieves well over 90% efficiency for most practical situations. Extensive simulation studies concur with this observation under a wide range of scenarios.     

Earthquakes occurrences estimation through a parametric semi-Markov approach

The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.     

A grouped beta process model for multivariate resting‐state EEG microstate analysis on twins

EEG microstate analysis investigates the collection of distinct temporal blocks that characterize the electrical activity of the brain. Brain activity within each microstate is stable, but activity switches rapidly between different microstates in a nonrandom way. We propose a Bayesian nonparametric model that concurrently estimates the number of microstates and their underlying behaviour. We use a Markov switching vector autoregressive (VAR) framework, where a hidden Markov model (HMM) controls the nonrandom state switching dynamics of the EEG activity and a VAR model defines the behaviour of all time points within a given state. We analyze the resting‐state EEG data from twin pairs collected through the Minnesota Twin Family Study, consisting of 70 epochs per participant, where each epoch corresponds to 2 s of EEG data. We fit our model at the twin pair level, sharing information within epochs from the same participant and within epochs from the same twin pair. We capture within twin‐pair similarity, using an Indian buffet process, to consider an infinite library of microstates, allowing each participant to select a finite number of states from this library. The state spaces of highly similar twins may completely overlap while dissimilar twins could select distinct state spaces. In this way, our Bayesian nonparametric model defines a sparse set of states that describe the EEG data. All epochs from a single participant use the same set of states and are assumed to adhere to the same state switching dynamics in the HMM model, enforcing within‐participant similarity.     

Non-parametric maximum likelihood estimation of interval-censored failure time data subject to misclassification

The paper considers non-parametric maximum likelihood estimation of the failure time distribution for interval-censored data subject to misclassification. Such data can arise from two types of observation scheme; either where observations continue until the first positive test result or where tests continue regardless of the test results. In the former case, the misclassification probabilities must be known, whereas in the latter case, joint estimation of the event-time distribution and misclassification probabilities is possible. The regions for which the maximum likelihood estimate can only have support are derived. Algorithms for computing the maximum likelihood estimate are investigated and it is shown that algorithms appropriate for computing non-parametric mixing distributions perform better than an iterative convex minorant algorithm in terms of time to absolute convergence. A profile likelihood approach is proposed for joint estimation. The methods are illustrated on a data set relating to the onset of cardiac allograft vasculopathy in post-heart-transplantation patients.     

Fitting the additive model by recursion on dimension

We consider estimation for the homoscedastic additive model for multiple regression. A recursion is proposed in Opsomer (1999), and independently by the authors, for obtaining the estimators that solve the normal equations given by Hastie and Tibshirani (1990). The recursion can be exploited to obtain the asymptotic bias and variance expressions of the estimators for any p > 2 (Opsomer 1999) using repeated application of Opsomer and Ruppert (1997). Opsomer and Ruppert (1997) provide asymptotic bias and variance for the estimators when p = 2. Opsomer (1999) also uses the recursion to provide sufficient conditions for convergence of the backfitting algorithm to a unique solution of the normal equations. However, since explicit expressions for the solution to the normal equations are not given, he states, “The lemma does not provide a practical way of evaluating the existence and uniqueness of the backfitting estimators … ”. In this paper, explicit expressions for the estimators are derived. The explicit solution requires inverses of n × n matrices to solve the np × np system of normal equations. These matrix inverses are feasible to implement for moderate sample sizes and can be used in place of the backfitting algorithm.     

Nonparametric inference and uniqueness for periodically observed progressive disease models

In many studies examining the progression of HIV and other chronic diseases, subjects are periodically monitored to assess their progression through disease states. This gives rise to a specific type of panel data which have been termed “chain-of-events data”; e.g. data that result from periodic observation of a progressive disease process whose states occur in a prescribed order and where state transitions are not observable. Using a discrete time semi-Markov model, we develop an algorithm for nonparametric estimation of the distribution functions of sojourn times in a J state progressive disease model. Issues of uniqueness for chain-of-events data are not well-understood. Thus, a main goal of this paper is to determine the uniqueness of the nonparametric estimators of the distribution functions of sojourn times within states. We develop sufficient conditions for uniqueness of the nonparametric maximum likelihood estimator, including situations where some but not all of its components are unique. We illustrate the methods with three examples.