Estimation of upper limits using a Poisson statistic

Bayesian, classical, and extended maximum-likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a Poisson statistic. A new approach is proposed, based on the statistical significance of a signal rather than on the number of events in the signal region. Application of these techniques is illustrated using a toy model.     

Parameter and Quantile Estimation for the Generalized Pareto Distribution

The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.     

用多项式模型和自适应滤波估计瞬时频率

本文论述了非平稳信号瞬时频率(IF)的估计方法,包括基干最小均方误差(LMS)算法或递推最小二乘(RLS)算法的自适应IF估计方法和基于信号相位多项式模型的IF估计方法。对各种估计方法的估计方差与理论方差下限进行了比较。说明了,基于互Wigner分布的估计方法所需信噪比(SNR)门限值最低。在低SNR、短信号记录的情况下,用多项式相位模型与最大似然法可以获得比较可靠的IF估计。     

Maximum likelihood Estimation of Parameters in the Inverse Gaussian Distribution,With Unknown Origin

Maximum likelihood estimation is applied to the three-parameter Inverse Gaussian distribution, which includes an unknown shifted origin parameter. It is well known that for similar distributions in which the origin is unknown, such as the lognormal, gamma, and Weibull distributions, maximum likelihood estimation can break down. In these latter cases, the likelihood function is unbounded and this leads to inconsistent estimators or estimators not asymptotically normal. It is shown that in the case of the Inverse Gaussian distribution this difticulty does not arise. The likelihood remains bounded and maximum likelihood estimation yields a consistent estimator with the usual asymptotic normality properties. A simple iterative method is suggested for the estimation procedure. Numerical examples are given in which the estimates in the Inverse Gaussian model are compared with those of the lognormal and Weibull distributions.     

基于UKF的非齐次泊松跳跃市场微结构模型研究

本文针对不确定性因素引起资产价格的巨大波动,构建了一个由非齐次泊松过程驱动的跳跃市场微结构模型.在模型参数未知的情况下,我们使用非参数化方法检测出时变跳跃强度,由此再利用无迹卡尔曼滤波和极大似然法来估计跳跃市场微结构模型参数的值.模拟仿真与实证分析验证了该方法的有效性,并利用AIC准则对两类跳跃波动率模型进行了优劣比较.研究结果表明,跳跃市场微结构模型在拟合股指数据方面要优于跳跃随机波动模型.     

A Problem of Ranking and Estimation With Poisson Processes

There are given k Poisson processes with parameters (rates of occurrence) λ₁, …, λ _k . Let λ₍₁₎ ≤ λ₍₂₎ ≤ … ≤ λ_(k) denote the ordered set of values of the parameters. A procedure is given for selecting the process corresponding to λ_(k) and estimating its parameter (λ_(k)). The given procedure controls the joint risk of improper selection and of large error in the estimate. Let θ > 1 and 0 < α, β < 1 be given numbers, and let δ denote the estimate of λ_(k). The joint probability that a correct selection is made and that |(δ/λ_(k)) ? 1| ≤ α is at least as large as β, for (λ_(k)/λ_(k?1)) ≥ θ. Two cases are considered, that is, when the processes are observed continuously in time, and when they are observed at successive intervals of time. Both the cases lead to the same theoretical results.     

Relationship Between System Failure Rate and Component Failure Rates

A simple sufficient condition is given for a system to have an increasing failure rate when the identical components comprising it have an increasing failure rate. Systems which function if and only if at least k of the n components function (“k out of n” systems) satisfy this condition. For systems of non-identical components, upper and lower bounds on failure rate are obtained in terms of component failure rates. These bounds are increasing functions of time for “k out of n” structures having components with increasing failure rates.     

非线性结构的参数估计和系统识别

非线性结构的参数估计和系统识别是取得和验证非线性结构数学模型的一门学科.本文综述了国内外非线性结构参数估计和系统识别的发展状况,较系统地介绍了非线性结构的数学模型、单自由度、多自由度系统的参数估计方法和非参数模型的识别方法.     

数字采样测量噪声误差的估计和分析

针对高频数字采样中的附加噪声和时间抖动误差估计问题，给出了高频数字采样测量噪声误差的最大似然估计方法。在获得了相应的数学模型后，对最小二乘估计和最大似然估计方法进行了比较。仿真结果表明，对于此类误差最大似然估计比最小二乘估计有效性更好。另外最大似然估计的一个优点是用于不确定度计算的克拉美一罗下限值更易于获得。     

电流变减振器的参数估计与减振性能研究

本文对研制的多层极板式电流变减振器进行了正弦和随机激励实验，发现这种减振器在低频时减振效果非常明显，在高电场时减振器表现出明显的非线性特性，减振器还具有移频特性，即减振器的刚度在电场作用下发生变化。为了比较，对一种滑动极板减振器进行了对比实验。最后用递归最小平方法估计了减振器的粘性阻尼和库仑阻尼，估计时考虑了刚度的变化，估计的结果与实验结果一致。     

Estimation of Variance Components in Two-Stage Nested Designs With Composite Samples

If the cost of measurement is high, it is often expedient to composite several samples before taking measurements. Optimal designs for estimating (individually and jointly) the mean and variance components in two-stage nested designs are discussed, using the so-called analysis of variance estimation procedure. This traditional procedure is then compared numerically with two other unbiased estimation procedures; specific conditions are given whereby a particular procedure is superior to the other procedures.     

A simultaneous equations model of crash frequency by severity level for freeway sections

This paper presents a simultaneous equations model of crash frequencies by severity level for freeway sections using five-year crash severity frequency data for 275 multilane freeway segments in the State of Washington. Crash severity is a subject of much interest in the context of freeway safety due to higher speeds of travel on freeways and the desire of transportation professionals to implement measures that could potentially reduce crash severity on such facilities. This paper applies a joint Poisson regression model with multivariate normal heterogeneities using the method of Maximum Simulated Likelihood Estimation (MSLE). MSLE serves as a computationally viable alternative to the Bayesian approach that has been adopted in the literature for estimating multivariate simultaneous equations models of crash frequencies. The empirical results presented in this paper suggest the presence of statistically significant error correlations across crash frequencies by severity level. The significant error correlations point to the presence of common unobserved factors related to driver behavior and roadway, traffic and environmental characteristics that influence crash frequencies of different severity levels. It is found that the joint Poisson regression model can improve the efficiency of most model coefficient estimators by reducing their standard deviations. In addition, the empirical results show that observed factors generally do not have the same impact on crash frequencies at different levels of severity.     

多元Marshall～Olkin型指数分布的特征及其参数估计

导出了多元Marshall～Olkin型指数分布的一个特征,利用该特征,获得了多元Marshall～Olkin型指数分布参数的最大似然估计及矩估计.     

Investigation of time and weather effects on crash types using full Bayesian multivariate Poisson lognormal models

Previous research shows that various weather elements have significant effects on crash occurrence and risk; however, little is known about how these elements affect different crash types. Consequently, this study investigates the impact of weather elements and sudden extreme snow or rain weather changes on crash type. Multivariate models were used for seven crash types using five years of daily weather and crash data collected for the entire City of Edmonton. In addition, the yearly trend and random variation of parameters across the years were analyzed by using four different modeling formulations. The proposed models were estimated in a full Bayesian context via Markov Chain Monte Carlo simulation. The multivariate Poisson lognormal model with yearly varying coefficients provided the best fit for the data according to Deviance Information Criteria. Overall, results showed that temperature and snowfall were statistically significant with intuitive signs (crashes decrease with increasing temperature; crashes increase as snowfall intensity increases) for all crash types, while rainfall was mostly insignificant. Previous snow showed mixed results, being statistically significant and positively related to certain crash types, while negatively related or insignificant in other cases. Maximum wind gust speed was found mostly insignificant with a few exceptions that were positively related to crash type. Major snow or rain events following a dry weather condition were highly significant and positively related to three crash types: Follow-Too-Close, Stop-Sign-Violation, and Ran-Off-Road crashes. The day-of-the-week dummy variables were statistically significant, indicating a possible weekly variation in exposure. Transportation authorities might use the above results to improve road safety by providing drivers with information regarding the risk of certain crash types for a particular weather condition.     

参数估计法测定多孔介质热湿迁移特性的实验研究

设计了基于参数估计法测定多孔介质热湿迁移特性的实验测试装置，在多孔介质局部含湿量和温度的实验测试数据基础上的波动通过参数估计算法得到了砂土的热湿迁移特必数据，此外，还对参数估计算法中的几个问题进行了分析探讨。     

Analysis of Field Return Data With Failed-But-Not-Reported Events

Warranty data contain valuable information on product field reliability and customer behaviors. Most previous studies on analysis of warranty data implicitly assume that all failures within the warranty period are reported and recorded. However, the failed-but-not-reported (FBNR) phenomenon is quite common for a product whose price is not very high. Ignorance of the FBNR phenomenon leads to an overestimate of product reliability based on field return data or an overestimate of warranty cost based on lab data or tracking data. Being an indicator of customer satisfaction, the FBNR proportion provides valuable managerial insights. In this study, statistical inference for the FBNR phenomenon as well as field lifetime distribution is described. We first propose a flexible FBNR function to model the time-dependent FBNR behavior. Then, a framework for data analysis is developed. In the framework, both semiparametric and parametric approaches are used to jointly analyze warranty claim data and supplementary tracking data from a follow-up of selected customers. The FBNR problem in the tracking data is minimal and thus the data can be used to effectively decouple the FBNR information from the warranty claim data. The proposed methods are illustrated with an example. Supplementary materials for this article are available online.     

多孔介质质扩散系数的参数估计方法及测定方法

提出一种在第三类边界条件下,通过使数值计算的湿分蒸发与规律实测值之间的最佳逼近,以瞬态确定计算多孔介质质扩散系数的参数估计方法。设计并制造了对流蒸发实验装置。在假设质扩散系数为含湿量线性函数的情况下,对石膏板和水泥板的质扩散系数进行了测量和计算。测试及计算方法简单可行,测定时间较稳态方法大大缩短,因此比较实用。     

同时测定含湿多孔介质热湿迁移特性的参数估计法

将含湿多孔介质瞬态温度场和湿度场的理论解与测量介质中某些点处的温度值和湿度值相结合，提出了一种同时测定含湿多孔介质热湿迁移特性的参数估计法。它可以通过一次实验获得多个迁移特性的数据，为发展多孔介质热湿迁移特性综合测量装置奠定了基础。     

基于线热源模型结合参数估计计算岩土热物性方法探讨

介绍了地源热泵空调系统中基于线热源模型结合参数估计法下的4种岩土热物性计算方法,结合工程实例对比分析了这4种方法的计算结果。建议在实际工程中采用三参数估计法来计算岩土导热系数、钻孔内热阻和岩土容积比热容为妥。     

多元线性正态SRM参数估计的渐近协方差阵及其估计

针对多元线性正态结构关系模型（SRM）,本文给出了真值向量协方差阵的广义逆构造,并在三种常见误差协方差阵假定下应用标准5法分别给出了模型结构参数约束最小二乘估计的渐近协方差阵及其相合估计。