推广的Pickands型估计量渐近正态的充要条件（英文）

估计量的研究是数理统计的一个重要方向,设计好的估计量一直是相关研究工作者的一项重要工作。渐近正态性作为评价估计量好坏的基本标准之一,是众多经典估计量所具有的性质。针对一类Pickands估计量,利用极值理论和顺序统计量极限性质,在较弱条件下获得了Pickands估计量渐近正态分布的充要条件,为该估计量的工程应用提供指导。     

极值指数之推广矩估计量的渐近正态性

首先将推广矩估计量代换为一种新的估计量,然后研究由该估计量引起的一种与尾经验过程有关的函数的弱收敛问题,最后得到与推广矩估计量有关的一随机过程的弱收敛函数,同时也就得到了推广矩估计量的渐近分布,因而证明了推广估计量的渐近正态性.     

关于正规变换函数性质的研究

正规变换函数是研究估计量的各类渐近性质的重要工具，在估计量的渐近性质研究中起着非常重要的作用。通过对正规变换函数性质的研究，利用概率统计的分析方法，对正规变换函数的性质做出更为深刻的刻画，推广了正规变换函数的性质，得到了正规变换函数的一系列好的性质，为极值理论领域中估计量及估计量各类性质的研究提供了有力的工具。     

恒定应力部分加速寿命试验的可靠性分析

基于定时区间删失样本,研究了指数分布产品在恒定应力部分加速寿命试验下的参数估计。利用EM算法得到了分布参数和加速因子的迭代方程。根据Louis提出的缺失信息原则计算了Fisher信息矩阵。由极大似然估计的渐近正态性,构造出分布参数和加速因子的近似置信区间。通过Monte Carlo模拟,从平均相对误差和均方误差两方面对估计量进行了计算,结果表明所有的估计量都具有大样本性质。最后通过模拟样本,计算了不同应力水平下分布参数、加速因子和可靠度的估计。     

广义逆指数分布元件的可靠性分析

在II型混合截尾样本下,得到了广义逆指数分布未知参数的最大似然估计。利用最大似然估计的渐近正态性构造了参数的渐近置信区间,运用Lindley's逼近方法和TierneyKadane's逼近方法计算出了参数的Bayes估计。最后,运用Monte-Carlo方法对上述估计方法结果作了模拟比较。     

贮存寿命分析中一种改进模型的参数估计

从贮存寿命分析中提出了一种改进模型,考虑了模型的参数估计问题。证明了估计量的相合性与渐近正态性。     

一种新的非参数谱估计方法

提出了一种新的非参数谱密度估计方法,它是传统加窗周期谱估计方法的一种修正,并证明了此估计具有渐近无偏性、相合性、渐近正态性.     

火控系统最大误差与参数极值的统计评定

系统误差的最大值和各种参数的极大值、极小值是系统研究设计、制造与使用者最关心的参数,而且使用中观念混乱与错误甚多。对正态随机参数,国际上有规定,国内尚未推行;对其它型参数,极值本身就是个随机变量,它服从Gumbel分布。从六十年代以来,用Gumbel统计方法研究,计算极值已有广泛应用。本文就火控系统中应用的工程方法,较系统地进行综合,并举例说明之。我国广泛应用Gumbel统计方法研究极值参数,有益于系统研究水平和安全性的提高。     

基于时滞分割法的具有leakage项时滞的离散型神经网络状态估计

摘要：研究一类具有leakage时滞的离散型神经网络的状态估计问题．通过构造新的Lyapunov泛函得到保证估计误差全局渐近稳定的充分条件,并通过求解一个线性矩阵不等式（LMI）得到状态估计器的增益矩阵．采用一种新的时滞分割方法将变时滞区间分割为多个子区间,使该结果在获得更小的保守性同时也降低了计算的复杂度．     

高可靠性软件的极值统计分析

提出了极值统计分析的方法.对于失效数据极值分布函数的拟合检验,采用了相关系数法;对于母体分布的参数估计,则分别采用了最小二乘估计(LSE)和极大似然估计(MLE);最后通过一个实例说明了统计过程,并用模拟的方法证明了最小二乘估计较好.     

Exact expected values of variance estimators for simulation

We formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady‐state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first‐order autoregressive process and the M/M/1 queue‐waiting‐time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The logistic–exponential survival distribution

For various parameter combinations, the logistic–exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub‐shaped failure rate, and upside‐down bathtub‐shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three‐parameter version is less mathematically tractable, our major results concern the two‐parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed‐point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two‐parameter and the three‐parameter versions of the logistic–exponential distribution are applied to two real‐life data sets. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

不同损失函数下指数-泊松分布的Bayes估计

基于定数截尾样本,在熵损失、Linex损失和刻度平方损失函数下,给出了指数-泊松分布参数的Bayes估计,并证明了所给估计都是容许的。最后给出了随机模拟例子,对所给估计结果的优良性进行了分析比较。     

Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model

Instead of measuring a Wiener degradation or performance process at predetermined time points to track degradation or performance of a product for estimating its lifetime, we propose to obtain the first‐passage times of the process over certain nonfailure thresholds. Based on only these intermediate data, we obtain the uniformly minimum variance unbiased estimator and uniformly most accurate confidence interval for the mean lifetime. For estimating the lifetime distribution function, we propose a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, these estimators and the above‐mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times. Thus, our method of using only intermediate data is useful for highly reliable products when their failure times are difficult to obtain. Furthermore, we show that the proposed new estimator of the lifetime distribution function is more accurate than the standard and modified maximum likelihood estimators. We also obtain approximate confidence intervals for the lifetime distribution function and its percentiles. Finally, we use light‐emitting diodes as an example to illustrate our method and demonstrate how to validate the Wiener assumption during the testing. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

指数寿命产品可靠性增长试验的Bayes分析

针对指数寿命产品的定时、定数截尾试验方案,推广了Mazzuchi-Soyer模型的应用范围。首先引入模型假设,以狄氏分布作为先验分布,综合利用产品研制的历史信息和专家信息,结合产品研制各阶段试验数据,给出了各阶段可靠性的联合后验分布。然后利用Gibbs抽样算法解决后验推断计算问题,得到各阶段产品可靠性的Bayes点估计和区间估计。最后给出产品可靠性增长分析实例,表明了模型的优越性。     

Asymptotic properties of imperfect repair models and estimation of repair efficiency

The aim of this articles is to study the asymptotic behavior of two imperfect repair models, called Arithmetic Reduction of Intensity and Arithmetic Reduction of Age models. These models have been proposed by Doyen and Gaudoin (Reliab Eng Syst Safe 84 (2004) 45–56) and include many usual virtual age models. First, it is proved that the failure intensity of these models is asymptotically almost surely equivalent to a deterministic increasing function with a cumulative error proportional to a logarithm. Second, the almost sure convergence and asymptotic normality of several estimators of repair efficiency are derived, when the wear‐out process without repair is known. Finally, the coverage rate of the asymptotic confidence intervals issued from those estimators is empirically studied. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Online process mean estimation using L1 norm exponential smoothing

A basic assumption in process mean estimation is that all process data are clean. However, many sensor system measurements are often corrupted with outliers. Outliers are observations that do not follow the statistical distribution of the bulk of the data and consequently may lead to erroneous results with respect to statistical analysis and process control. Robust estimators of the current process mean are crucial to outlier detection, data cleaning, process monitoring, and other process features. This article proposes an outlier‐resistant mean estimator based on the L₁ norm exponential smoothing (L₁‐ES) method. The L₁‐ES statistic is essentially model‐free and demonstrably superior to existing estimators. It has the following advantages: (1) it captures process dynamics (e.g., autocorrelation), (2) it is resistant to outliers, and (3) it is easy to implement. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

宽带目标回波模型的物理解释及小波变换表示

在点目标回波模型基础上,通过对理想运动体目标的分析,引入了距离-速度联合分布密度和时延-时间伸缩联合分布密度函数的概念,详细推导了延展目标的宽带回波模型,解释了各密度函数和宽带扩展函数的物理意义及相互关系,最后给出了宽带回波模型的小波变换表示方法.