特征变量优选在苹果可溶性固形物近红外便携式检测中的应用

为实现苹果可溶性固形物(SSC)的便携式快速检测,利用环形光纤探头和微型光谱仪搭建便携式苹果可溶性固形物光谱采集系统,结合无信息变量消除(UVE)、遗传算法(GA)、竞争性自适应加权(CARS)算法筛选基于偏最小二乘(PLS)的苹果可溶性固形物的近红外光谱特征波长。另外,采用反向区间最小二乘支持向量机(BiLS-SVM)和GA算法优选基于LS-SVM的特征波长变量,分别建立所选特征波长和全波段的PLS模型和LS-SVM模型。试验结果表明,经过GA-CARS算法从全波段1 512个波长中筛选出的50个特征波长建立的PLS模型效果最好,其预测相关系数和预测均方根误差分别为0.962和0.403°Brix。利用该检测装置结合GA-CARS筛选的特征波长,可有效简化苹果可溶性固形物近红外便携式检测模型并提高模型的预测精度,为进一步构建便携式苹果可溶性固形物检测设备奠定了基础。     

高光谱技术结合CARS算法的库尔勒香梨可溶性固形物定量测定

由于高光谱数据量大、维数高,光谱噪声明显、散射严重等特征导致光谱建模时关键变量提取较为困难,同时,高光谱图像的获取会受非单色光、杂散光、温度等多种因素的影响,从而使高光谱数据与待测性质之间有一定非线性关系。为此,提出采用正自适应加权算法(CARS)对可见-近红外高光谱高维数据进行关键变量筛选,并与全光谱和经典变量提取方法SPA,MC-UVE,GA和GA-SPA方法进行比较。以200个库尔勒香梨为研究对象,采用SPXY方法将样本划分为校正集和预测集,校正集和预测集分别包含150个和50个样本。基于不同方法筛选的变量,分别建立线性PLS模型及非线性LS-SVM模型,r2,RMSEP和RPD用于模型性能的评估。综合比较发现,GA,GA-SPA和CARS变量筛选方法能够有效地筛选出原始高光谱数据中具有强信息且对外界影响因素不敏感的变量,适用于高光谱数据关键变量的提取,其中CARS变量筛选效果最佳,基于CARS获取的关键变量构建的非线性LS-SVM库尔勒香梨SSC含量预测模型获得了最优的预测结果,r2_pre,RMSEP和RPD分别为0.851 2,0.291 3和2.592 4。研究表明,CARS方法是一种有效的高光谱关键变量筛选方法,利用高光谱数据,非线性LS-SVM模型比线性PLS模型更适合于香梨品质的定量预测。     

我国封闭式投资基金业绩评价实证研究

随着我国基金行业超常发展,恰当的分析和评价基金业绩已越来越重要。本文根据CAPM的基本原理,利用国外先进的基金业绩评价方法对我国封闭式基金的综合业绩进行实证研究。研究结果表明:总体来看,基金获得的市场超额收益显著为负。基金经理不具有证券选择能力,但具有一定的市场择时能力,但这两种能力均不显著。同时,我们还发现不同投资风格的基金经理具有不同的证券选择能力和市场择时能力。     

Practical arbitrage‐free scenario tree reduction methods and their applications in financial optimization

We construct an arbitrage‐free scenario tree reduction model, from which some arbitrage‐free scenario tree reduction algorithms are designed. They ensure that the reduced scenario trees are arbitrage free. Numerical results show the practicality and efficiency of the proposed algorithms. Results for multistage portfolio selection problems demonstrate the necessity and importance for guaranteeing that the reduced scenario trees are arbitrage free, as well as the practicality of the proposed arbitrage‐free scenario tree reduction algorithms for financial optimization.     

Non-Convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a nonconvex optimization problem. This article shows a remarkable result: despite the nonconvexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of nonconvex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for nonconvex optimization and a novel way of exploiting nonconvexity for statistical inference.     

多阶段应急决策的方案链选择方法

针对多阶段不同情景下多指标多任务的应急决策问题,提出了一种方案链选择方法。在该方法中,首先给出了决策方案链的概念,并对多阶段多指标多任务的应急决策问题进行了描述;然后根据相邻阶段的子方案之间的相容性,构建了相容性关系矩阵;进一步地,在考虑相邻阶段子方案之间相容性的情形下,以各阶段的子方案的综合评价值最大为目标,建立了应急决策的方案链选择的优化模型。通过求解模型,得到应急决策的最优方案链。最后,通过一个算例说明了该方法的可行性和有效性。     

Is breaking of ensemble equivalence monotone in the number of constraints?

Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian.     

Optimal uncertainty size in distributionally robust inverse covariance estimation

In a recent paper, Nguyen et al. (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this estimator. We develop a statistical theory which shows how to optimally choose the uncertainty size to minimize the associated Stein loss. Surprisingly, rather than the expected canonical square-root scaling rate, the optimal uncertainty size scales linearly with the sample size.     

基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题

本文研究了均值-方差优化准则下,保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程,保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务(如再保险).本文的限制条件为投资和再保险策略均非负,即不允许卖空风险资产,且再保险的比例系数非负.除此之外,本文还引入了新巴塞尔协议对风险资产进行监管,使用随机二次线性(linear-quadratic,LQ)控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程不再有古典解.在粘性解的框架下,我们给出了新的验证定理,并得到有效策略(最优投资策略和最优再保险策略)的显式解和有效前沿.     

Existence of solutions for integral inclusions of Urysohn type with nonconvex-valued orientor field

In this paper, we prove the existence of solutions for an integral inclusion of Urysohn type with nonconvex orientor field and with delay. We make standard boundedness and continuity assumptions on the data, and we assume that the orientor field is l.s.c. in the state variable. Using a selection theorem of Fryszkowski, we are able to prove the existence of solutions, extending an earlier result of Angell.This research was supported by NSF Grant No. DMS-86-02313.