变换法在解微分方程中的应用

变量代换法是解常微分方程的一种辅助方法，它能使问题简化．本文通过联系实例给出了变换在求解微分方程中的具体应用。     

我国工业电力用户价值画像模型构建与应用研究

在新型冠状病毒感染肺炎疫情对我国电力市场造成巨大冲击的宏观背景下,为进一步提升我国供电企业营销服务资源配置效能,最大化撬动供电企业的综合效益,笔者开展了我国工业电力用户价值画像模型研究。本文对电力用户价值进行了分析和定义,从安全稳定价值(S)、经济效益价值(E)、契约信用价值(C)与有序用电价值(O)四个维度,构建了我国工业电力用户价值评级SECO指标模型,并集成智能算法中的RST(粗糙集理论)与数据挖掘技术中的PAM(围绕中心点切割聚类算法),构造了一种半监督自动化用户价值识别、预测与特征展示模型,模型包括基于RST的指标体系设计、基于Gower相异度系数与PAM的用户价值评级,以及基于用户画像的价值特征展示三大模块。其中,为增强聚类分析结果的科学性与可靠性,采用霍普金斯统计量进行聚类趋势判断,利用间隔统计量输出理论最佳聚类数目,运用轮廓系数评估模型效果与识别误判样本。以我国南方电网公司下属某供电企业电力用户数据进行模型测试与应用研究,得到具有较高解释性与区分度的用户细分方案,表明本模型是一套可行有效的用户价值评级与特征可视化工具。     

二维变系数线性微分系统的求解定理

给出二维变系数线性微分系统在已知某解的情形下求通解的公式,并直接应用此公式,导出几类二维变系数线性微分系统的通解公式.对理论和实际应用都是有益的.     

A Study to Improve the Method of Ascertaining Attribute Weight Based on Rough Sets Theory

There are some shortages to ascertain attribute weight based on rough set in current studies. In this paper, attrib- ute importance represented by rough set is studied deeply. Aiming at the existing problems, algebra presentation of rough sets is proved to be more comprehensive than its information presentation, then a new method of ascertaining attribute weigh is put forward based on rough set conditional entropy. Finally, it is shown that the new method is more reasonable than the old one by an example.     

Variable precision rough set theory and data discretisation: an application to corporate failure prediction

Since the seminal work of Pawlak (International Journal of Information and Computer Science, 11 (1982) 341–356) rough set theory (RST) has evolved into a rule-based decision-making technique. To date, however, relatively little empirical research has been conducted on the efficacy of the rough set approach in the context of business and finance applications. This paper extends previous research by employing a development of RST, namely the variable precision rough sets (VPRS) model, in an experiment to predict between failed and non-failed UK companies. It also utilizes the FUSINTER discretisation method which neglates the influence of an ‘expert’ opinion. The results of the VPRS analysis are compared to those generated by the classical logit and multivariate discriminant analysis, together with more closely related non-parametric decision tree methods. It is concluded that VPRS is a promising addition to existing methods in that it is a practical tool, which generates explicit probabilistic rules from a given information system, with the rules offering the decision maker informative insights into classification problems.     

Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

综合选择指数中的变量选择

本文首次从变量选择的角度把ＡＩＣ准则应用于动物性状的综合选择指数之中,从而获得了最佳的综合选择指数。     

Oracle Inequalities for Convex Loss Functions with Nonlinear Targets

This article considers penalized empirical loss minimization of convex loss functions with unknown target functions. Using the elastic net penalty, of which the Least Absolute Shrinkage and Selection Operator (Lasso) is a special case, we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear, this inequality also provides an upper bound of the estimation error of the estimated parameter vector. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear, we give sufficient conditions for consistency of the estimated parameter vector. We briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions covered by our framework.     

In-Sample Inference and Forecasting in Misspecified Factor Models

This article considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension-reduction devices: principal components, ridge, Landweber Fridman, and partial least squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross-validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting inflation and output growth in the U.S. show that data-reduction methods outperform conventional methods in several relevant settings, and might effectively guard against instabilities in predictors’ forecasting ability.     

Instrumental variable based variable selection for generalized linear models with endogenous covariates

We study the variable selection problem for a class of generalized linear models with endogenous covariates. Based on the instrumental variable adjustment technology and the smooth-threshold estimating equation (SEE) method, we propose an instrumental variable based variable selection procedure. The proposed variable selection method can attenuate the effect of endogeneity in covariates, and is easy for application in practice. Some theoretical results are also derived such as the consistency of the proposed variable selection procedure and the convergence rate of the resulting estimator. Further, some simulation studies and a real data analysis are conducted to evaluate the performance of the proposed method, and simulation results show that the proposed method is workable.