基于HTFWGBM算子的供应商选择模型研究

由于供应商选择中的的复杂性与不确定性以及人类认知的有限性,从而导致信息融合失真和决策结果不准确的情况。针对决策属性以犹豫三角模糊数（HTFN）给出的供应商的选择问题,本文提出一种基于HTFGWBM算子的决策算法。首先,针对犹豫三角模糊数和几何Bonferroni平均算子理论,分别定义了犹豫三角模糊几何Bonferroni平均（HTFGBM）算子和犹豫三角模糊几何加权Bonferroni平均（HTFGWBM）算子,同时分别研究了算子的幂等性,置换不变性,单调性和有界性等性质。其次,基于HTFGWBM算子构建新型犹豫多属性决策模型,结合HTFN排序方法进行备选供应商排序。最后通过算南水北调中线工程中的供应商选择实例证明了决策模型的可行性与有效性。结果表明,通过调整模型参数,模型具有一定的延展性和容错能力,能够很好的进行科学决策。     

改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型,针对不确定环境下的投资组合问题,把证券的收益率、风险损失率和流动性用区间数描述,建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次,为求解该模型,提出了改进的区间可接受度确定性转换方法,通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后,通过数值实验将提出的方法与传统方法进行比较,结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。     

求解输出为有界随机数的排序择优问题

目的/意义排序择优问题是仿真优化领域的经典研究问题。该问题的目标是设计统计采样算法,通过在有限个统计分布中进行采样并观测随机采样结果从而找到真实均值最大的分布。在该问题的研究中,现有文献大多假设对不同分布进行采样时输出为正态分布随机数,进而基于正态分布随机数相关性质进行算法设计。但在现实中,该假设通常不成立,一旦假设不成立,现有算法的统计有效性将会大受影响。设计/方法将正态假设进行拓展,即假设对不同分布为有界域分布,进而开展算法设计。结论/发现设计出一类顺序淘汰式算法求解输出为有界域随机数的排序择优问题,数值实验验证,此算法效率远高于现有的SE、ME和lil′DCB算法。     

高新技术创新的文化路径及政策选择

相对一般的技术创新，高新技术创新有其独有的一些特点，这些特点决定了文化对高新技术创新具有重要作用。高新技术创新的文化路径包括观念文化路径、制度文化路径和行动文化路径三个方面。基于文化视角优化高新技术创新的政策选择，完善我国科技政策，有助于推动高新技术的进一步创新。     

A likelihood ratio test to discriminate exponential–Poisson and gamma distributions

The exponential–Poisson (EP) distribution with scale and shape parameters β>0 and λ∈?, respectively, is a lifetime distribution obtained by mixing exponential and zero-truncated Poisson models. The EP distribution has been a good alternative to the gamma distribution for modelling lifetime, reliability and time intervals of successive natural disasters. Both EP and gamma distributions have some similarities and properties in common, for example, their densities may be strictly decreasing or unimodal, and their hazard rate functions may be decreasing, increasing or constant depending on their shape parameters. On the other hand, the EP distribution has several interesting applications based on stochastic representations involving maximum and minimum of iid exponential variables (with random sample size) which make it of distinguishable scientific importance from the gamma distribution. Given the similarities and different scientific relevance between these models, one question of interest is how to discriminate them. With this in mind, we propose a likelihood ratio test based on Cox's statistic to discriminate the EP and gamma distributions. The asymptotic distribution of the normalized logarithm of the ratio of the maximized likelihoods under two null hypotheses – data come from EP or gamma distributions – is provided. With this, we obtain the probabilities of correct selection. Hence, we propose to choose the model that maximizes the probability of correct selection (PCS). We also determinate the minimum sample size required to discriminate the EP and gamma distributions when the PCS and a given tolerance level based on some distance are before stated. A simulation study to evaluate the accuracy of the asymptotic probabilities of correct selection is also presented. The paper is motivated by two applications to real data sets.     

Quadratic Approximation via the SCAD Penalty with a Diverging Number of Parameters

The high-dimensional data arises in diverse fields of sciences, engineering and humanities. Variable selection plays an important role in dealing with high dimensional statistical modelling. In this article, we study the variable selection of quadratic approximation via the smoothly clipped absolute deviation (SCAD) penalty with a diverging number of parameters. We provide a unified method to select variables and estimate parameters for various of high dimensional models. Under appropriate conditions and with a proper regularization parameter, we show that the estimator has consistency and sparsity, and the estimators of nonzero coefficients enjoy the asymptotic normality as they would have if the zero coefficients were known in advance. In addition, under some mild conditions, we can obtain the global solution of the penalized objective function with the SCAD penalty. Numerical studies and a real data analysis are carried out to confirm the performance of the proposed method.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

Transductive versions of the LASSO and the Dantzig Selector

Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO.     

Model Checks in Inverse Regression Models with Convolution‐Type Operators

Abstract. We consider the problem of testing parametric assumptions in an inverse regression model with a convolution‐type operator. An L ₂ ‐type goodness‐of‐fit test is proposed which compares the distance between a parametric and a non‐parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non‐parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017.