高维数据下群组变量选择的惩罚方法综述

变量选择是统计建模的重要环节,选择合适的变量可以建立结构简单、含义明确、预测精准的稳健模型。在实际应用中,有些变量具有群组结构,本文概括了三类群组变量选择惩罚方法,包括处理高度相关变量、仅选择组变量、即选择组又选择单个变量的方法,着重比较了它们的统计性质和优缺点,总结了相关算法和调整参数选择的方法。最后文章归纳了相关应用情况,并讨论了最新发展方向和所面临的挑战。     

基于改进粒子群算法的模糊聚类-概率神经网络模型的企业财务危机预警模型研究

为了充分发挥概率神经网络在企业财务危机预警中的作用,克服概率神经网络平滑参数难以确定和空间复杂度高的不足,本文提出一类新的参数动态调整的粒子群算法优化概率神经网络的平滑参数,进而采用改进粒子群算法优化初始隶属度矩阵的模糊聚类方法实现对样本的选择,解决了概率神经网络平滑参数的确定及空间结构复杂的问题。提出了基于改进粒子群算法的模糊聚类-概率神经网络企业财务危机预警模型,并以我国上市公司作为研究对象进行了实证研究。结果表明,经过模糊聚类和改进粒子群算法优化的概率神经网络具有更优的预测性能,并在企业财务危机长期预警方面具有一定效用。     

缺失数据下半参数变系数部分线性模型的统计推断

该文研究协变量随机缺失下半参数变系数部分线性模型的统计推断.利用逆概率加权最小二乘方法给出了模型中参数分量和非参数分量的估计,并证明了它们的渐近正态性.另外该文又提出了一个逆概率加权经验对数似然比统计量,并证明该统计量服从标准χ~2分布,从而构造了模型中参数分量的经验似然置信域.最后通过模拟研究和实例分析说明该文提出的方法具有较好的有限样本性质.     

垂直裂缝气井生产动态预测及参数识别

为了摆脱分析解释水力压裂裂缝参数时选择图版的繁复工作和克服人为的误差,在引入非达西因子的基础上,考虑裂缝导流能力在生产过程中的变化,提出了垂直裂缝气井中真实气体在地层-裂缝系统中非达西渗流的数学模型和生产动态预测模型,建立了识别垂直裂缝气井水力裂缝参数的生产历史自动拟合模型,并给出了数值解法,为认识和了解气层、分析和评估气井压裂施工质量,提供了准确可靠的方法。     

统计收敛与概率测度

早在1951年,H.F ast[6]就引入了统计收敛的定义.之后,出现了许多相关文章(如[4,7-14]等)对统计收敛做了进一步的探索与研究.自上世纪末本世纪初以来,统计收敛作为活跃的领域而得到了深入的研究.例如,统计收敛在数值理论[5],三角级数[15],强可和性[3],局部凸空间[10,13]以及局部紧空间中有界连续函数的理想结构[2]等领域中的讨论.本文通过引入μ-稠密收敛和μ-统计收敛的定义,对于给定一类概率测度U,证明了μ∈U,则序列μ-稠密收敛与统计收敛等价;对μ∈U,序列统计收敛必μ-统计收敛;μ∈U,序列都μ-统计收敛当且仅当序列统计收敛.     

基于蚁群算法的模糊分类系统设计

提出了一种基于最大-最小蚁群算法的模糊分类系统设计方法.该方法通过两个阶段来实现:特征变量选择和模型参数优化.首先采用蚁群算法对特征变量进行选择,得到一组具有较高分辩性能的特征变量,提高模型的解释性;在模型结构确定后,蚁群算法从训练样本中提取信息对模型的参数进行优化,在保证模型精确性的前提下,构造具有较少变量数目及规则数目的模糊模型,实现了精确性与解释性的折衷.最后将本方法运用到Iris和Wine数据样本分类问题中,并将结果与其它方法进行比较,仿真结果证明了该方法的有效性.     

函数型二次模型的假设检验

本文研究了函数型二次回归中二次参数函数的显著性检验问题。采用函数型主成分分析将预测变量函数进行投影降维,利用零模型和全模型的残差平方和构造F型检验统计量。在一定的正则条件下证明了检验统计量在原假设下渐近于F分布,在备择假设下检验统计量依概率趋于无穷,从而表明该检验方法是相合的。进一步证明了在一定收敛速度的局部备择假设下,检验统计量渐近于非中心F分布。最后通过数值模拟研究了该检验方法在有限样本下的表现,并给出了一个实际例子进一步验证所提方法的有效性。     

多组样本下GL—统计量的渐近性质

本文主要讨论多组样本下GL－统计量的渐近分布,这里我们使用了Gateaut微分逼近方法,在多组i.i.d.样本下,给出了GL－统计量的渐近正态分布的一组条件,从而拓广了i.i.d样本下GL－统计量的渐近正态分布的性质[1]。     

两多维样本模型中位置参数相等性的M-检验

本文给出了基于投影寻踪方法检验两多维样本位置参数相等的M 统计量和t 统计量,分别用PP型自助M 统计量和PP型自助t 统计量给出了上述两统计量的近似分布, 并给出了检验的算法,进行一些模拟.     

缺失数据下线性模型的半参数估计

通过比较参数方法和非参数方法对选择概率建模的优缺点,基于充分降维的思想提出了一种利用单指标模型对选择概率建模的半参数方法.基于逆概率加权方法和半参数方法,研究了缺失数据下线性模型的统计推断问题.建立的逆概率加权估计方程可以处理不同的数据缺失情形,给出了线性模型中兴趣参数的估计,并证明了它的渐近正态性.最后通过模拟研究说明提出的方法具有较好的有限样本性质.     

Using population of models to investigate and quantify gas production in a spatially heterogeneous coal seam gas field

In this work, we discuss the use of a local model developed previously [1] that describes the multiphase flow of gaseous species and liquid water within a single coal seam to investigate the gas production from a spatially heterogeneous production field. The field is located within the Surat Basin in Queensland, and is composed of a total of 80 production wells spread over a region covering approximately 36 km². However, not every well is producing gas at any one time and so in this work we take a subset of 42 wells that are the top-producing wells in terms of total gas volume.We utilise a population of models approach to understand the variability in the underlying physical processes, and as a mechanism for dealing with the spatial heterogeneity that arises due to geological variation across the field. We are able to simultaneously obtain a family of parameter sets for each of these wells, in which each set in the family yields a predicted cumulative total gas production curve that matches the measured cumulative production curve for a given well to within an allowable limit of error.By analysing the results of this population of models approach we can identify the similarities between wells based on the parameter distributions, and understand the sensitivity of key model parameters. We show by example that high correlation between wells based on their parameter values may be an indicator of their similarity. A combinatorial sum of the predicted gas production is compared against the individual gas volumes (given in terms of percentage of the total volume) measured at the compression facility as a way of further calibrating a subpopulation of models.     

Stochastic model of phase transition and metastability

The evolution of a system with phase transition is simulated by a Markov process whose transition probabilities depend on a parameter. The change of the stationary distribution of the Markov process with a change of this parameter is interpreted as a phase transition of the system from one thermodynamic equilibrium state to another. Calculations and computer experiments are performed for condensation of a vapor. The sample paths of the corresponding Markov process have parts where the radius of condensed drops is approximately constant. These parts are interpreted as metastable states. Two metastable states occur, initial (gaseous steam) and intermediate (fog). The probability distributions of the drop radii in the metastable states are estimated. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 94–106, April, 2000.     

Bid calculation for construction projects: Regulations and incentive effects of unit price contracts

The Austrian contract awarding system for construction projects is characterized by the unit price contract being an important contract type. The bid price is a decisive criterion for the selection of the construction company that performs a project, and the bid price is calculated from the unit prices and the specified production volumes of the project activities. Since the actual production volumes can differ from the specified volumes, the actual payment can differ from the bid price according to these deviations. In practice there can be asymmetric information on the production volumes. This leads to an incentive for the bidders to “skew” the bid calculation by asymmetric allocation of overhead costs to project activities.In this paper we analyze this agency-theoretical situation and develop a model that decides on the allocation of overhead costs to project activities in order to maximize the actual payment for a predetermined bid price. We also present a case study and comment on the implications of the model for the contract awarding system in the construction industry.     

Comparison and correction of the drop breakup models for stochastic dilute spray flow

Spray–gas interaction is common in many industrial applications that use a liquid jet injection system. Numerous liquid drops interact with the surrounding gas as they travel through the air. During such a travel, aerodynamic interaction between a drop and the surrounding gas flattens the drop and ultimately, breaks up the drop. The TAB (Taylor Analogy Breakup) model was proposed by O’Rourke and Amsden (1987) [6] for the KIVA spray code, but the use of this model has been controversial because the original paper that proposed this model has typographical errors. Another well-known drop breakup model, such as the DDB (Drop Deformation Breakup) model of Ibrahim et al. (1993) [8], has been widely used. However, although numerical solutions of the DDB model ostensibly make it appear superior to those of other previous breakup models, they contain errors that need to be amended. This paper aims to clarify the error controversies of both models; the typographical errors and the erroneous numerical solutions. The complete mathematical derivation of the TAB model is presented, and its correct numerical solutions are compared against the experimental data. We found that the TAB model was superior to other breakup models, such as Clark (1988) [7] and DDB.     

Small Ball Probabilities for a Shifted Poisson Process

We investigate the probabilities of hitting shifted small balls by sample paths of a centered Poisson process and find the exact range of parameters for which the Wiener approximation of these probabilities is valid. Towards this aim, we introduce the Skorokhod density technique. For the Poisson process, this technique plays a role similar to that of the Cameron-Martin formula in the construction of associated laws for a Gaussian measure. Bibliography: 20 titles.     

Numerical analysis for bulk-arrival queueing systems: Root-finding and steady-state probabilities inGI r /M/1 queues

Queueing theorists have presented, as solutions to many queueing models, probability generating functions in which state probabilities are expressed as functions of the roots of characteristic equations, evaluation of the roots in particular cases being left to the reader. Many users have complained that such solutions are inadequate. Some queueing theorists, in particular Neuts [6], rather than use Rouché's theorem to count roots and an equation-solver to find them, have developed new algorithms to solve queueing problems numerically, without explicit calculation of roots. Powell [7] has shown that in many bulk service queues arising in transportation models, characteristic equations can be solved and state probabilities can be found without serious difficulty, even when the number of roots to be found is large. We have slightly modified Powell's method, and have extended his work to cover a number of bulk-service queues discussed by Chaudhry et al. [1] and a number of bulk-arrival queues discussed in the present paper.     

应用模糊综合评判和灰色关联度分析评价水平井多级压裂效果

水平井多级压裂是低渗透和非常规油气田开发的有效技术手段,其压后产能评价问题已成为相关研究的热点和难点.水平井多级压裂压后产能的各项影响因素之间关系复杂,通过常规理论分析量化研究困难,压裂效果很难准确预测.本文提出应用模糊综合评判和灰色关联度分析相结合的方法,对多级压裂水平井的压裂效果进行评价.首先运用灰色理论分析影响压裂效果的各因素之间的灰色关联度,计算各影响因素在综合评判中的权重值,再结合模糊综合评判方法,对多级压裂井压后效果进行预测评价.通过目的区块24口多级压裂水平井压后效果评价与实际生产情况对比,表明模型计算准确率达到95.8%,评价结果准确可靠.     

Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions

Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distribution, J. Multivariate Anal. 21 (2003) 69-78] but somewhat more in the spirit of Fourdrinier et al. [On the construction of bayes minimax estimators, Ann. Statist. 26 (1998) 660-671] for the normal case, in the sense that we construct classes of priors giving rise to minimaxity. A feature of this paper is that in certain cases we are able to construct proper Bayes minimax estimators satisfying the properties and bounds in Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264]. We also give some insight into why Strawderman's results do or do not seem to apply in certain cases. In cases where it does not apply, we give minimax estimators based on Berger's [Minimax estimation of location vectors for a wide class of densities, Ann. Statist. 3 (1975) 1318-1328] results. A main condition for minimaxity is that the mixing distributions of the sampling distribution and the prior distribution satisfy a monotone likelihood ratio property with respect to a scale parameter.     

两参数Weibull分布参数的联合置信区间

本文推广了文献[1]的方法,给出了定数截尾情况下两参数Weibull分布的形状参数的区间估计,并通过大量的Monte-Carlo模拟考察了优选问题。另外还讨论了两参数的联合区间估计。文章最后通过实例说明了本文方法的应用。