Estimating the common location parameter of exponential distributions with censored samples

Consider the problem of estimating the common location parameter of two exponential distributions when censored samples are taken. The unique minimum variance unbiased estimator (UMVUE) is found along with an expression for its variance. The asymptotic distribution is given for a special case and a generalized Bayes property is exhibited. Extensions include the case of k > 2 populations. Also the UMVUE is found for P(Y > X) and certain reliability functions.     

The effects of model parameter deviations on the variance of a linearly filtered time series

We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

教学质量评价中协方差分析的应用

协方差分析是在方差分析与回归分析基础上发展起来的一种统计方法 ,通过对考试成绩的方差分析与协方差分析结果的比较 ,探讨协方差分析在教学效果评价中的作用。     

A bivariate normal theory maximum-likelihood technique when certain variances are known

A maximum-likelihood technique is described for estimating the bivariate normal distribution of the estimates of two or more related values when data are obtained from several different sources, each having known variance. The problem is comparable, in the bivariate sense to estimating the mean of a normal population with known variance. The results tend to be dominated by those sources of data associated with the smallest variances.     

The variance of the coverage of a randomly located area target by a salvo of weapons

We derive formulas for the variance of that proportion of the value of a randomly located, circularly symmetric area target that is destroyed by N independently fired weapons of identical type whose damage functions are circularly symmetric about the respective impact points. The probability density functions of the target center location and of the weapon impact points are also circularly symmetric. The general results are specialized to uniform and Gaussian functions. In the latter case a closed-form solution (triple integral) for the variance of the coverage is derived. Similar to some well-known results on expected coverage, this expression for the variance of the coverage can be easily evaluated by numerical quadrature. Numerical results are given which indicate the target coverage variability caused by the combined effects of random target-locating errors and weapon impact point fluctuations.     

基于拉盖尔模型的超声信号渡越时间测量性能分析

传统窄带模型仅能通过数值计算统计出超声信号渡越时间的测量性能。针对这一问题,提出基于拉盖尔模型计算理论克拉下限的方法。研究了拉盖尔函数及其时间导数的性质,得到时间导数内积矩阵,并将其应用到费舍尔矩阵中,能够快速精确计算克拉下限。对混合指数模型仿真表明,在高斯白噪声背景下,渡越时间方差与理论克拉下限具有良好的一致性;受窄带噪声和反射等因素影响,实测数据的渡越时间方差与理论克拉下限存在较大偏差。     

模糊随机变量的模糊概率特征的性质

应用模糊数理论 ,给出了模糊随机变量的数学期望和模糊随机变量的方差的定义 ,并研究讨论了模糊随机变量的数学期望和模糊随机变量的方差的性质。研究结果进一步丰富和完善了模糊随机变量理论。     

Consistency of several variants of the standardized time series area variance estimator

In statistical analysis of stationary time series or in steady-state simulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the area estimator of standardized time series, namely, the weighted area and the Cramér-von Mises area estimators, and provide their consistency, in the strong sense and mean-square sense. A sharp bound for the (asymptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a rate of convergence of this estimator, as well as a confidence interval for the variance parameter. © 1995 John Wiley & Sons, Inc.     

Optimal design of accelerated life tests under periodic inspection

For the exponentially distributed lifetimes, optimal accelerated life test plans are determined under the assumptions of periodic inspection and Type I censoring. Computational results indicate that for the range of parameter values considered the asymptotic variance of the estimated mean or pth quantile at the use stress is not sensitive to the number of inspections at overstress levels. Senstivity analyses are also conducted to see how senstive the asymptotic variance of the estimated mean is with respect to the uncertainties involved in the guessed failure probabilities at the use and high stress levels. Computational results show that moderate deviations (several tens of percents) of the guessed failure probabilities from their true values are fairly tolerable in terms of the relative amount of increase in the asymptotic variance of the estimated mean. Procedures for selecting a sample size and for determining whether or not to conduct an accelerated life test are also discussed.     

方差全局灵敏度求解的空间分割结合无迹变换方法

为有效计算基于方差的全局灵敏度指标尤其是非线性程度较高的响应函数的,将积分空间的可加性以及无迹变换结合起来,利用函数在子空间内非线性程度会降低以及无迹变换方法在概率空间内对低非线性函数性质具有强捕捉能力的特点,提出计算基于方差的全局灵敏度指标的高效方法。该方法只需产生一组无迹变换样本就可以近似求得各阶灵敏度指标,并且该近似解随空间分割个数的增加而收敛于真值。通过非线性程度较高的验证算例及工程算例验证了所提方法在处理非线性功能函数上的高效性和准确性。     

ISAR成像包络对齐性能评估

运动补偿是ISAR成像中的关键技术,通常包括包络对齐和相位补偿,而包络对齐是相位补偿的基础。现有包络对齐方法较多,在无法直观判断包络对齐效果的情况下,需要进行定量评估,以选择最优的对齐方法用于ISAR成像。提出基于距离单元方差的包络对齐评估方法:以对齐后各距离单元方差的加权和作为评估指标,对包络对齐结果直接进行评估。进行了相应的仿真实验,结果证明了该评估方法的有效性。     

Probabilistic priorities in the M/G/1 queue

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.     

Research on simultaneous localization and mapping for AUV by an improved method: Variance reduction FastSLAM with simulated annealing

At present, simultaneous localization and mapping (SLAM) for an autonomous underwater vehicle (AUV) is a research hotspot. Aiming at the problem of non-linear model and non-Gaussian noise in AUV motion, an improved method of variance reduction fast simultaneous localization and mapping (FastSLAM) with simulated annealing is proposed to solve the problems of particle degradation, particle depletion and particle loss in traditional FastSLAM, which lead to the reduction of AUV location estimation accuracy. The adaptive exponential fading factor is generated by the anneal function of simulated annealing algorithm to improve the effective particle number and replace resampling. By increasing the weight of small particles and decreasing the weight of large particles, the variance of particle weight can be reduced, the number of effective particles can be increased, and the accuracy of AUV location and feature location estimation can be improved to some extent by retaining more information carried by particles. The experimental results based on trial data show that the proposed simulated annealing variance reduction FastSLAM method avoids particle degradation, maintains the diversity of particles, weakened the degeneracy and improves the accuracy and stability of AUV navigation and localization system.     

不完全量测下基于面目标的火控系统性能分析

针对实际工程中出现的不完全量测下火控系统性能的理论研究,将水面舰船建模为椭圆形面目标,建立了不完全量测下基于面目标测量的数学模型,给出了火控跟踪系统统计意义下的估计误差Cramer-Rao下界(CRLB);根据目标状态与射击诸元间的非线性误差传递关系,基于UT变换得到不完全量测下基于面目标的火控系统射击诸元误差方差下界。以某型舰载火控系统为例,仿真结果表明,在不完全量测下,与传统的质点目标火控系统相比,基于面目标测量的火控系统在估计性能上提高36%,火控性能提高34%。     

方差分量的Bayes二次无偏估计及可容许估计的非负性

对于有P 个方差分量的线性模型,本文导出了方差分量线性函数的Bayes 不变二次无偏估计的显示表达式,证明了Bayes 不变二次无偏估计类形成了可容许的不变二次无偏估计的完全类。在可容许的不变二次无偏估计类中,讨论了非负参数函数的非负估计问题,给出了可容许的非负定估计存在的充要条件。     

Combining standardized time series area and Cramér–von Mises variance estimators

We propose three related estimators for the variance parameter arising from a steady‐state simulation process. All are based on combinations of standardized‐time‐series area and Cramér–von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin–Watson statistic; and the third is related to a jackknifed version of the first. The main derivations yield analytical expressions for the bias and variance of the new estimators. These results show that the new estimators often perform better than the pure area, pure CvM, and benchmark nonoverlapping and overlapping batch means estimators, especially in terms of variance and mean squared error. We also give exact and Monte Carlo examples illustrating our findings.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

发动机粘接界面加速老化及寿命预测

介绍发动机粘接界面老化试验,根据其力学特性的变化,建立合适的数学模型,并估算出贮存寿命。     

随机截尾场合下步进应力加速寿命试验的统计分析

给出了随机截几场合下步进应力加速寿命试验（步加试验）的统计方法,并讨论了其估计的方差问题．     

控制性能评价与监控理论的研究进展

自Harris(1989)提出最小方差控制基准以来,控制性能评价与监控技术受到了极大的关注,并取得了大量的成果.学者们在最小方差基准的基础上提出了广义最小方差基准、用户定义基准、基于模型的基准等多种评价方法,并由最初的单输入单输出系统推广到了多输入多输出系统、时变系统等.仔细回顾了控制性能评价与监控理论的发展历程,并指出该领域面临的主要问题以及未来的发展方向.     

态势估计中一种基于贝叶斯估计的统计时间推理方法

统计时间推理是态势估计中的一个重要组成部分。Ｋｉｒｉｌｏｖ的基于极大似然估计（Ｍａｘｉ－ｍｕｍＬｉｋｅｌｉｈｏｏｄＥｓｔｉｍａｔｉｏｎ,ＭＬＥ）的推理方法将未知时间变量看作常数,估计方差较大。文中建立的已知时间信息和未知时间变量之间的关系模型,将未知时间变量扩展为随机变量,将贝叶斯估计（ＢａｙｅｓＥｓｔｉｍａｔｉｏｎ,ＢＥ）引入时间推理。经过对两种推理算法的性能进行分析和比较,发现在一定范围内,基于ＢＥ的方法性能优于基于ＭＬＥ的方法。