互反判断阵比对值对满意一致性的影响

满意一致性是互反判断阵可否作为决策依据的指标.对CR>1的互反判断阵,一般是通过比对值的修正,使之达到满意一致性要求.利用多元隐函数偏导数及行列式基本性质,可以得出各比对值变化对满意一致性的影响比例.在已知影响比例情况下,比对值如何修正、修正多少就有了理论上的依据.     

AHP的检验方法及其比较分析

介绍了目前较有影响的三种ＡＨＰ一致性检验算法,并对其作了比较分析,最后提出了一种检验算法的选择准则     

Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses

We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (\rho-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n): Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.     

基于一致性的制造业企业伙伴选择多属性决策模型研究——合作创新视角

为解决制造业企业合作创新伙伴选择问题,将单一评价方法与组合评价方法相结合,提出了基于一致性的制造业企业合作创新伙伴选择组合评价方法。在构建制造业企业合作创新伙伴选择评价指标体系基础上,应用基于一致性的组合评价方法对某汽车制造业企业合作创新伙伴选择组合评价,得到了一致性和收敛性的评价结论,验证了基于一致性方法的科学性、合理性和有效性。基于一致性的组合评价方法一定程度上解决了组合评价结论的非一致性问题,不仅可以达到组合评价结果取长补短的效果,而且能够充分利用多层次信息,更加贴近评价对象的全貌,为多属性决策问题提供了新思路。     

On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.     

Robust Model Averaging Method Based on LOF Algorithm

Model averaging is a good alternative to model selection, which can deal with the uncertainty from model selection process and make full use of the information from various candidate models. However, most of the existing model averaging criteria do not consider the influence of outliers on the estimation procedures. The purpose of this paper is to develop a robust model averaging approach based on the local outlier factor (LOF) algorithm which can downweight the outliers in the covariates. Asymptotic optimality of the proposed robust model averaging estimator is derived under some regularity conditions. Further, we prove the consistency of the LOF-based weight estimator tending to the theoretically optimal weight vector. Numerical studies including Monte Carlo simulations and a real data example are provided to illustrate our proposed methodology.     

Likelihood adaptively modified penalties

A new family of penalty functions, ie, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study the stability properties of the penalized maximum‐likelihood estimator, 2 types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate‐descent algorithm is proposed. Simulation results and real data analysis show that the proposed approach has competitive performance in comparison with the existing methods.     

固定设计下一类半参数回归模型的渐近性质

对固定设计下的一类半参数回归模型yi=xiβ+g(xi)+ei,i=1,2,…,n,综合最小二乘和非参数权函数估计方法,定义了,βg的估计量β∧n,gn∧及误差方差σ2的估计量σ2n∧.在适当条件下,证明它们具有强相合性和p(2)阶平均相合性.模拟的结果表明所得结果具有优良的性质.     

Asymptotic Properties of Nonparametric Kernel Regression Estimator for \rho-Mixing Samples

For \rho-mixing samples, we discuss thestrong consistency of the nonparametric kernel regression estimator proposed by Gasser and Muller. Under more weaker conditions, its strong consistency and uniformly strong consistency are proved.     

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??For \rho-mixing samples, we discuss thestrong consistency of the nonparametric kernel regression estimator proposed by Gasser and Muller. Under more weaker conditions, its strong consistency and uniformly strong consistency are proved.     

Property (ω) and Its Perturbations

In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index.In addition,the stability of property(ω) for H(P) operators is considered.     

Bootstrap bandwidth selection in kernel density estimation from a contaminated sample

In this paper we consider kernel estimation of a density when the data are contaminated by random noise. More specifically we deal with the problem of how to choose the bandwidth parameter in practice. A theoretical optimal bandwidth is defined as the minimizer of the mean integrated squared error. We propose a bootstrap procedure to estimate this optimal bandwidth, and show its consistency. These results remain valid for the case of no measurement error, and hence also summarize part of the theory of bootstrap bandwidth selection in ordinary kernel density estimation. The finite sample performance of the proposed bootstrap selection procedure is demonstrated with a simulation study. An application to a real data example illustrates the use of the method. This research was supported by ‘Projet d’Actions de Recherche Concertées’ (No. 98/03-217) from the Belgian government. Financial support from the IAP research network nr P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is also gratefully acknowledged.     

NA样本最近邻密度估计的相合性

在NA样本下研究最近邻密度估计的相合性，给出弱相合性、强相合性、一致强相合性以及它们的收敛速度的充分条件．同时研究了失效率函数估计的一致强相合性     

混合误差半参数回归模型估计的相合性

研究了误差为ψ混合和ψ混合序列的半参数回归模型,综合最小二乘法和非参数权函数估计方法,分别定义了待估参数β和未知函数夕的估计量βm,n和9m,n(χ).利用混合序列的矩不等式及凸函数的性质,在较弱的条件下证明了这些估计量的强相合性与矩相合性,这些结果推广了已有的相应的研究结果.     

基于乘性一致性残缺互补判断矩阵的决策方法

对于满足乘性一致性的残缺互补判断矩阵的决策问题,提出了一种决策方法。首先把互补判断矩阵的乘性一致性定义进行了简化,得到了互补判断矩阵乘性一致性的另外几种表达形式;进一步得到了在已知n-1个特殊元素的条件下,残缺互补判断矩阵中缺失元素的补全方法;然后给出了残缺互补判断矩阵可接受的条件,以及矩阵的一致性检验及调整方法;基于残缺互补判断矩阵,给出了以下决策步骤:残缺互补判断矩阵的一致性检验及调整过程,补全缺失元素的迭代过程和最优方案择优过程。最后给出了一个实例,通过该实例的计算以及本文方法与已有方法的比较,证明了本文方法是简便和有效的。     

一类零膨胀广义线性模型极大似然估计的相合性与渐近正态性

讨论了响应变量为单参数指数族且在零点处膨胀的广义线性模型的大样本性质,对其参数进行了极大似然估计,给出了一些正则条件.基于所提出的正则条件,证明了模型参数极大似然估计的相合性与渐近正态性.     

On Least Squares Estimation for Stable Nonlinear AR Processes

Following a Markov chain approach, this paper establishes asymptotic properties of the least squares estimator in nonlinear autoregressive (NAR) models. Based on conditions ensuring the stability of the model and allowing the use of a strong law of large number for a wide class of functions, our approach improves some known results on strong consistency and asymptotic normality of the estimator. The exact convergence rate is established by a law of the iterated logarithm. Based on this law and a generalized Akaike's information criterion, we build a strongly consistent procedure for selection of NAR models. Detailed results are given for familiar nonlinear AR models like exponential AR models, threshold models or multilayer feedforward perceptions.     

NA样本递归型分布函数估计的相合性

在NA相依样本条件下，对未知分布函数F(x)的递归核估计进行研究，在适当的条件下，得到了估计的r^-阶平均相合速度，逐点强相合和一致强相合速度，作为应用，讨论了平均剩余寿命函数估计的相合速度。     

基于模糊互补判断矩阵的一致性调整新方法

针对模糊互补判断矩阵的乘性一致性问题,本文从模糊乘性一致矩阵的定义出发, 首先给出了一种衡量判断矩阵一致性程度的新指标,然后综合利用专家给出的直接判断信息和间接判断信息,提出了一种改善模糊互补判断矩阵一致性的新方法,最后通过一个算例说明了此方法的可行性和简洁性.     

Limit Consistent Solutions in Noncooperative Games

Strong and limit consistency in finite noncooperative games are studied. A solution is called strongly consistent if it is both consistent and conversely consistent (Ref. 1). We provide sufficient conditions on one-person behavior such that a strongly consistent solution is nonempty. We introduce limit consistency for normal form games and extensive form games. Roughly, this means that the solution can be approximated by strongly consistent solutions. We then show that the perfect and proper equilibrium correspondences in normal form games, as well as the weakly perfect and sequential equilibrium correspondences for extensive form games, are limit consistent.