Partially function linear error-in-response models with validation data

This paper considers partial function linear models of the form Y =∫X(t)β(t)dt + g(T)with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.     

Approximate conditional likelihood for generalized linear models with general missing data mechanism

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate. Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.     

含不确定参数线性优化的新鲁棒优化模型

针对椭球不确定数据鲁棒线性优化模型的保守性,提出了一种新的鲁棒线性优化模型。通过引入新的距离公式,把椭球不确定数据映射到单位球中,以此来改进鲁棒线性优化模型。新模型克服了原模型对数据扰动较大时的保守性,从而在解的鲁棒性和最优性之间得到一个比较好的平衡。通过对几个标准实际问题的测试,结果表明新模型在保证解的鲁棒性的同时具有良好的最优性。     

故障拓展模型到概率检验模型的转换规则

以故障拓展模型和概率检验模型为基础,通过分析概率检验模型的语法语义、转移命令及逻辑关系,研究清晰、完整的转换规则,实现故障拓展模型向概率检验模型的转换。此外,研究模型的定量概率检验转换规则,构建逻辑验证表达。最后,对机载通信系统调谐控制功能展开基于概率检验的定量安全性评估。结果表明,通过将故障拓展模型转换为概率检验模型的转换规则,能够实现复杂系统定量安全性自动分析,从而有效支持航空器复杂系统安全性评估过程。     

Sieve least squares estimator for partial linear models with current status data

Current status data often arise in survival analysis and reliability studies, when a continuous response is reduced to an indicator of whether the response is greater or less than an observed random threshold value. This article considers a partial linear model with current status data. A sieve least squares estimator is proposed to estimate both the regression parameters and the nonparametric function. This paper shows, under some mild condition, that the estimators are strong consistent. Moreover, the parameter estimators are normally distributed, while the nonparametric component achieves the optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed estimates. For illustration purposes, the method is applied to a real dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.     

线性生成的一般模糊线性系统

基于结构元方法,研究了由对称模糊结构元线性生成的一般模糊线性系统和双重的一般模糊线性系统的求解问题,并给出了系统解存在的充要条件. 同时给出了这类模糊线性系统在工程、经济领域的应用实例.     

一种基于残差熵的动态模型检验方法

针对时间序列的模型检验与定阶问题,构造了一种新的统计量“残差熵”。该物理量融合了随机序列的相关性和信息论中信源熵的思想,综合反映了残差中所残留的信息量。在正态假设的基础上推导了模型“残差熵”的估算公式,并给出了具体的应用方法。实例计算表明:“残差熵”可用于模型的检验和定阶,极小化残差熵是一种有效的模型检验准则,并与经典的模型检验准则做了性能比较。     

Empirical likelihood confidence region for parameters in linear errors-in-variables models with missing data

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin (1976) is considered in this paper. A constrained empirical likelihood confidence region for a parameter β ₀ in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β ₀. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation’s conclusion.     

基于统计模型检测的DFT定量分析方法

动态故障树(dynamic fault tree, DFT)是对系统进行安全性分析的重要手段,基于马尔可夫链的DFT求解方法存在3个难题:一是仅可分析故障概率为指数分布的系统;二是无法分析共因失效情况;三是可能导致状态空间爆炸。因此提出一种基于统计模型检测的DFT定量分析方法。首先将DFT分解为动态逻辑门、基本构件、共因失效关系、门门和门构件间的逻辑关系;其次将动态逻辑门、基本构件和共因失效关系基于随机混成自动机形式化规约;然后通过逻辑关系重构自动机,形成随机混成自动机网络;最后通过分析一个具有共因失效关系的服从多失效概率分布的飞机结冰探测系统,表明所提方法的有效性。     

基于描述逻辑的能力需求模型验证方法

针对C⁴ISR系统能力需求模型中存在的一致性和合理性问题,提出了一种能力需求模型的验证方法。先采用基于描述逻辑的本体描述语言OWL DL精确描述能力需求分析中的元概念模型和应用概念模型,然后在元概念模型和应用概念模型之上附加一定的模型验证推理规则,并通过符号推理系统验证了能力概念的完整性以及目标的一致性。     

考虑右删失数据的改进Jelinski-Moranda软件可靠性模型

针对软件可靠性测试停止时间不对应失效的右删失问题,给出考虑完全右删失失效数据的改进Je-linski-Moranda(J-M)模型。定量分析了右删失失效数据对可靠性参数评估值的影响,在此基础上分别给出基于残存缺陷比率、失效率以及可靠度函数的软件可靠性测试停止准则。最后将改进模型应用于一组失效数据集,计算结果表明,改进后的模型可充分挖掘右删失数据中蕴含的时间信息,得到更准确的参数评估值。并且所提出的停止准则可有效指导软件可靠性测试活动的开展,具有较好的工程应用价值。     

基于Petri网模型检验的安全关键软件需求验证

需求形式化建模和模型检验可以提高安全关键软件的可信性,但在模型描述、调试和解释能力方面存在局限。对使用Petri网支持软件系统建模进行了扩展,设定默认值为零的权函数、利用“非”虚线描述在状态为假和变迁失败情况下的触发,增强阈值条件的描述能力,区分了枚举型和数值型库所,区分了普通迁移和强赋值迁移,并给出了扩展后的形式化定义及其和检验语言的语义映射。最后给出在典型机载软件上的应用,建立了软件需求模型和部分映射代码,对模型进行检验、反例路径分析和需求完善。过程和结果表明该方法可以有效的支持实际的关键安全软件需求建模和验证。     

移动核心网故障数据二重联合线性判别模型与应用

主要研究移动核心网BSC的TRAU数据分布规律及可疑故障识别方法.由于BSC的最大承载量是未知的, 因此本文定义了一类TRAU数据突增故障现象,并在此基础上定义了可疑故障点、异常点和广义异常点. 提出并建立了移动核心网故障数据二重联合线性判别模型和三类模式判别准则,用来对移动核心网TRAU数据进行三类模式("正常"、 "异常"、"可疑故障")识别.实例分析表明,本文所建立的移动核心网故障数据二重联合线性判别模型, 当用来对TRAU数据进行三类模式判别时,对原数据样本的回判和新数据样本的识别准确率都达到百分之百, 因此能有效识别TRAU数据中的可疑故障点.     

Novel encryption model for multimedia data

A novel encryption model is proposed. It combines encryption process with compression process, and realizes compression and encryption at the same time. The model’s feasibility and security are analyzed in detail. And the relationship between its security and compression ratio is also analyzed.     

非全数据EV模型的参数辨识及可靠性分析

对于在测量系统(Ⅰ)下分别测到n个数据值的n件产品，在测量系统(Ⅱ)下只测到其中的n1件产品，未测到的n2(n1 n2=n)件产品在使用了t1h后，需要在测量系统(Ⅱ)下做无替换定期检测，要求对这n2件产品作出可靠性分类，分类标准是与使用前相比其改变量不超过一个额定值．论文使用期望最大(EM)算法，对这种非全数据的变量含误差(EV)模型的参数给出了一种辨识方法，并给出了估计标准、错分概率及相应的错分代价，用此方法解决了某飞机发动机公司的高压涡轮叶片的寿命分析问题。     

Inference on coefficient function for varying-coefficient partially linear model

One important model in handling the multivariate data is the varying-coemcient partially linear regression model.In this paper,the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not.It is showed that the normalized proposed test follows asymptoticallyχ~2-distribution and the Wilks phenomenon under the null hypothesis,and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing.Some simulation studies illustrate that the test works well.     

一般分布区间型符号数据的描述统计与分析

以对大规模个体数据通过打包形成的区间型符号数据为研究对象, 针对个体在区间内往往不服从均匀分布的实际情况, 研究一般分布的区间型符号数据的描述统计和分析方法. 对符号数据分析进行了概述, 并定义了一般分布的区间变量. 研究了一般分布的区间变量的经验分布函数和经验联合分布函数. 在此基础上, 讨论了一般分布区间变量的描述统计量的求解. 最后给出了算例, 运用一般分布区间型符号数据的因子分析方法, 以中国股市为背景进行了应用研究. 结论表明: 以往研究基于均匀分布假设所给出的描述统计量的计算, 可看作文中所给求解公式的特例. 另外,研究方法基于经验分布理论, 无需知道个体在区间内服从分布函数的具体表达式, 且在计算过程中充分利用了区间内的个体信息.     

Asymtotics of Dantzig selector for a general single-index model

As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin’s paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.     

The ANOVA-type inference in linear mixed model with skew-normal error

Linear mixed effect models with skew-normal errors and distribution-free random effects are considered. The ANOVA-type F-tests are proposed to test the significance of random effects and the hypothesis on fixed effects of interest, respectively. Both tests are proved to be exact F-tests under this model, and the exact confidence interval for fixed effects of interest is derived. Simulation results are given to study the powers of ANOVA-type tests.     

Estimation in a semi-varying coefficient model for panel data with fixed effects

This paper considers a semi-varying coefficient model for panel data with fixed effects, proposes the profile-likelihood-based estimators for the parametric and nonparametric components, and establishes convergence rates and asymptotic normality properties for both estimators. Simulation results show that the proposed estimators behave well in finite sample cases.