余重对数二元模型的似然及惩罚似然估计

对３种抽样方式讨论了余重对数二元回归概率模型的极大似然估计和极大惩罚似然估计。并对数据及模型作了进一步的推广。     

惩罚似然中光滑参数λ的选取

半参数广义线性模型的基本分析采用极小惩罚似然法，而此回归曲面的惩罚似然估计又依赖于光滑参数λ的选取。对光滑参数λ的估计作出理论分析。     

一种新的感度试验与分析方法

介绍了一种新的感度试验设计与分析方法，即Ｎｅｙｅｒ法。它利用最大似然估计来选择下一个试验水平，利用似然比试验可计算任意置信区间，并以Ｃｒａｍｅｒ－Ｒａｏ理论为基础，可以分析所有感度试验结果。     

基于LSTM时间序列重建的生产装置异常检测

工业生产装置通常设置传感器报警阈值进行报警，但是对处于报警阈值以下的时间序列异常难以及时捕捉。基于统计的传统检测方法在解决时间序列异常检测上存在很大挑战，因此提出基于long short term memory (LSTM)时间序列重建的方法进行生产装置的异常检测。该算法首先引入一层LSTM网络对传感器数据的时间序列进行向量表示，采用另一层LSTM网络对时间序列进行逆序重建，然后利用重建值与实际值之间的误差，通过极大似然估计方法对该段序列进行异常概率估计，最终通过学习异常报警阈值实现时间序列异常检测。采用ECG测试数据、能源数据与危险品储罐传感器数据进行了仿真实验，验证了所提方法在不同长度的数据上的有效性。     

汽液相平衡测定中色谱数据的处理——最大似然函数法

采用气相色谱对几组物系的汽液相数据进行测定，用最大似然函数法对色谱数据进行处理。     

气体传感器Weibull分布下的一种有效参数估计

通过几种统计方法的比较,选用Weibull分布来对气体传感器的试验数据进行统计分析.针对Weibull分布的参数估计并结合气体传感器试验数据的特殊性,采用威布尔概率纸法和最小二乘法对试验数据进行初步处理,之后利用极大似然估计法对分布参数进行估计.     

概率论和数理统计在油气资源评价中的应用

概率论和数理统计在油气资源评价中应用可概括为油气藏/田规模概率分布规律研究、油气藏/田总体的预测、油气资源的回归分析预测和油气资源的蒙特卡罗模拟预测4个方面。文中讨论了对数正态分布和帕莱托分布两种主要的油气藏/田规模概率分布模型的特点、应用历史、理论基础以及对评价结果的影响;概述了最大似然理论、贝叶斯理论和不等概率抽样理论在油气藏/田总体预测中的应用;讨论了回归分析在油气的发现和生产的生命旋回模型和负指数变化模型中的应用;描述了资源评价的面积产率和体积产率法中蒙特卡罗模拟的应用。     

结构陶瓷弯曲强度的Weibull统计实验研究

本文在强度统计方法的Weibull模数估计及试样数量优化研究基础上,对氧化铝陶瓷进行了弯曲强度统计的大子样模拟母体试验,同时也对碳化硅、氮化硅、氧化铅增韧氧化铝等典型结构陶瓷进行了实验研究。实验结果表明,利用无偏极大似然估计的理论结果及置信度和相对误差双参数可以明确材料强度及其强度统计数据的精度。     

脆性材料强度统计分析中Weibull模数估计的试样数量的优化

为了全面的评价脆性材料强度特性指标,研究了强度统计方法中Weibull模数估计的试样数的优化问题。文中利用无偏极大似然估计理论结果,用置信度和相对误差双参数,计算出Weibull模数估计中的最优试样数,以便在Weibull模数估计试验中根据研究对象的要求,正确选用试样数量。文中结果在脆性材料强度特性评价与可靠性评价及其它适合Weibull统计的对象均可应用。     

基于伯恩斯坦多项式和D-vine copula的过程监控方法

针对利用Vinecopula进行过程故障监控的建模过程中二元Copula函数种类选择困难问题,提出一种基于惩罚伯恩斯坦多项式的D-vinecopula选择方法,运用到化工过程故障监控领域。该方法通过最近邻算法确定D-vine copula模型的变量顺序,利用惩罚伯恩斯坦多项式和核密度估计器分别估计得到D-vine copula的模型参数和单变量边缘概率密度函数,构成多元变量的联合概率分布。最后结合高密度区域与静态密度分位数表,构建广义局部概率指标,实现在线过程监控。该方法在田纳西-伊斯曼(TE)过程和醋酸脱水过程进行检验。综合故障检测率和误报率的统计结果,表明该方法有良好的监控性能。     

Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems

Abstract. This article describes a polynomial estimation technique based on the state‐space model and develops an estimation method for the quadratic estimation problem by applying the multivariate recursive least squares (RLS) Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete‐time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The augmented signal vector is modelled in terms of an autoregressive model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is found to be considerably improved in comparison with the existing RLS Wiener estimators. The proposed method may be applied advantageously to the quadratic estimations of wide‐sense stationary stochastic signals in general.     

On two-stage james-stein sstimators

In the context of minimum risk (point) estimation of the mean vector of a multivariate normal distribution, based on the James-Stein and an allied rule, a two stage procedure is considered, and the relative risk efficiency results are studied.     

Joint Determination of the State Dimension and Autoregressive Order for Models with Markov Regime Switching

Abstract. This paper is concerned with the problem of joint determination of the state dimension and autoregressive order of models with Markov‐switching parameters. A model selection procedure is proposed which is based on optimization of complexity‐penalized likelihood criteria. The efficacy of the procedure is evaluated by means of Monte Carlo experiments.     

On uniform integrability and asymptotically risk-efficient sequential estimation

In the theory of asymptotically risk-efficient sequential estimation, one encounters uniform integrability of both positive and negative powers of stopping rules and moment convergence of randomly stopped statistics. We describe a simple approach to obtain these uniform integrability and moment convergence results, not only in the classical setting of i.i.d. observations but also for much more general stochastic sequences. We also use this approach to establish asymptotic risk efficiency of sequential estimators of means of stochastic sequences and to derive asymptotic approximations for the mean squared errors of ratio estimators.     

Recursive estimation of quantitles using recursive kernel density estimators

Recursive estimation of quantiles may be obained via adaptive stochastic approximation

approximation theorms can be used to obtained the asympotic properties when the obervation are independent. for dependent sequences matingale theory cannot be applied straight forwardly as the tool for asympototic analysis.In this paper we consider both the case when the observation are i.i.d. and when they form a stationary and strongly regular process.the main result is sufficient condition for almost sure convergence in the strongly regular case.     

Unit Root Tests Based on Unconditional Maximum Likelihood Estimation for the Autoregressive Moving Average

Unconditional maximum likelihood estimation is considered for an autoregressive moving average that may contain an autoregressive unit root. The limiting distribution of the normalized maximum likelihood estimator of the unit root is shown to be the same as that of the estimator for the first-order autoregressive process. A likelihood ratio test based on unconditional maximum likelihood estimation is proposed. In a Monte Carlo study for the autoregressive moving-average model of order (1, 1), the new test is shown to have better size and power than those of several other tests.     

On sequentially adaptive asymptotically efficient rank statistics

For the simple regression model ( containing the two—sample location model as a special case ), adaptive ( linear ) rank statistics arising in the context of ( asymtotically) efficient testing and estimation procedures are considered. An orthonormal system based on the classical Legendre polynomial system is incorporated in the adaptive determination of the score generating function, and the proposed sequential procedure is based on a suitably posed stopping rule. Various properties of this sequentailly adaptive procedure and the allied stopping rule are studied. Asymptotic linearity results ( in a shift or regression parameter ) of linear rank statistics are studied with special reference to the Legendre polynomial system and some improved rates of convergence are estabilished in this context.     

Regularized maximum likelihood estimation of sparse stochastic monomolecular biochemical reaction networks

A sparse parameter matrix estimation method is proposed for identifying a stochastic monomolecular biochemical reaction network system. Identification of a reaction network can be achieved by estimating a sparse parameter matrix containing the reaction network structure and kinetics information. Stochastic dynamics of a biochemical reaction network system is usually modeled by a chemical master equation (CME) describing the time evolution of probability distributions for all possible states. This paper considers closed monomolecular reaction systems for which an exact analytical solution of the corresponding chemical master equation can be derived. The estimation method presented in this paper incorporates the closed-form solution into a regularized maximum likelihood estimation (MLE) for which model complexity is penalized. A simulation result is provided to verify performance improvement of regularized MLE over least-square estimation (LSE), which is based on a deterministic mass-average model, in the case of a small population size.     

The Local Bootstrap for Periodogram Statistics

A bootstrap procedure for the periodogram of a weakly dependent stationary sequence is proposed. The method works by locally resampling the periodogram ordinates and does not require estimation of the spectral density and of frequency domain residuals obtained by means of initial smoothing. Asymptotic properties of the proposed bootstrap procedure are studied and consistency is proved for interesting classes of statistics including ratio statistics, kernel estimates of the spectral density and parameter estimates. Some practical aspects concerning the implementation of the method are also discussed.     

Monitoring of an industrial wastewater plant employing finite‐time convergence observer

In this paper, the estimation of non measured variables (bioreactor biomass and settler biomass concentrations) is addressed. The plant is subjected to sudden step disturbances on the inlet oxygen flow, such that an observer with finite‐time convergence is required, to maintain adequate estimation performance. The observer structure contains a fractional power of the estimation error which is proposed to ensure the convergence properties needed. Under the assumptions considered, a mathematical analysis is performed to demonstrate the convergence of the estimation error and the convergence time is also calculated. The performance of the observer is illustrated with numerical experiments and compared with standard nonlinear Luenberger observer. Copyright © 2006 Society of Chemical Industry