A Survey of L1 Regression

L₁ regularization, or regularization with an L₁ penalty, is a popular idea in statistics and machine learning. This paper reviews the concept and application of L₁ regularization for regression. It is not our aim to present a comprehensive list of the utilities of the L₁ penalty in the regression setting. Rather, we focus on what we believe is the set of most representative uses of this regularization technique, which we describe in some detail. Thus, we deal with a number of L₁‐regularized methods for linear regression, generalized linear models, and time series analysis. Although this review targets practice rather than theory, we do give some theoretical details about L₁‐penalized linear regression, usually referred to as the least absolute shrinkage and selection operator (lasso).     

Tree networks to assess financial contagion

We propose a two-layered tree network model that decomposes financial contagion into a global component, composed of inter-country contagion effects, and a local component, made up of inter-institutional contagion channels. The model is effectively applied to a database containing time series of daily CDS spreads of major European financial institutions (banks and insurance companies), and reveals the importance of monitoring both channels to assess financial contagion. Our empirical application reveals evidence of a high inter-country and inter-institutional vulnerability at the onset of the global financial crisis in 2008 and during the sovereign crisis in 2011. The results identify France as central to the inter-country contagion in the Euro area during the financial crisis, while Italy dominates during the sovereign crisis. The application of the model to detect contagion between sectors of the European economy reveals similar findings, and identifies the manufacturing sector as the most central, while, at the company level, financial institutions dominate during the 2008 crisis.     

THE EFFECT OF ESTIMATION IN HIGH‐DIMENSIONAL PORTFOLIOS

We study the effect of estimated model parameters in investment strategies on expected log‐utility of terminal wealth. The market consists of a riskless bond and a potentially vast number of risky stocks modeled as geometric Brownian motions. The well‐known optimal Merton strategy depends on unknown parameters and thus cannot be used in practice. We consider the expected utility of several estimated strategies when the number of risky assets gets large. We suggest strategies which are less affected by estimation errors and demonstrate their performance in a real data example. Strategies in which the investment proportions satisfy an L₁ ‐constraint are less affected by estimation effects.     

EVA 考核下科技型央企价值创造能力影响因素研究——基于 Elastic Net 的实证研究

本文基于EVA视角以科技型央企为样本对象,收集其2011~2015年的面板数据为研究样本,选出影响央企价值创造能力的30个指标,运用弹性网的模型对其进行实证研究,并与Lasso模型及自适应Lasso模型进行对比,最终筛选出18个对EVA率产生关键影响的指标,并得到其回归系数,最后又将三种模型的准确率进行检测,得出资产报酬率和净资产利润率对央企价值创造能力的正向作用最为显著的结果,企业价值创造能力应着重从以上的方面进行评估。此外,本文从实证结果中得出结论：科技型央企应积极提高自身资产利用效率,谨慎使用权益资本进行投资,才能进一步提升自身价值创造能力。     

A Quantile Regression Analysis of the Effect of Farmers’ Attitudes and Perceptions on Market Participation

The objective of this study is to investigate the subjective determinants of farmers’ participation in output markets in five EU New Member States (NMS) characterised by large semi‐subsistence sectors. It employs quantile regression to model market participation reflecting the heterogeneity amongst farmers. The study also uses the Bayesian adaptive lasso to simultaneously select important covariates and estimate the corresponding quantile regression models. The empirical results show that only two variables affect all quantiles, while their effect varies across quantiles. Some of the remaining variables affect the share of output sold at the lower quantiles (i.e. for subsistence‐ and semi‐subsistence‐oriented farmers) only, whereas other variables are only significant at the upper quantiles (i.e. for more commercially oriented farms). Advisory services, and particularly agricultural business advice, and information and advice on markets and prices can facilitate the market participation of subsistence‐oriented farms.     

A kind of new time-weighted nonnegative lasso index-tracking model and its application

This study describes improved index-tracking methods to replicate the target index’s market performance in a high-dimensional sparse linear regression with nonnegative constraints on the coefficients. The main objective of this study is to construct a sparse portfolio with a better prediction effect and robustness. Considering the influence of time factors on index tracking, we propose a time-weighted nonnegative lasso index tracking model under different market constraints and define two new time-weighted construction methods. This index tracking model is an extension of Lasso and has variable selection consistency and estimation consistency under time-weighted nonnegative irrepresentable conditions similar to the irrepresentable condition in Lasso. We use the multiplicative updates algorithm to obtain the model’s solution since it is faster and simpler. The constrained index tracking problem in the stock market without short sales is studied in the latter part. The empirical results indicate that the optimized time-weighted nonnegative lasso index tracking model can obtain a smaller out-of-sample tracking error. The constructed portfolio has a better prediction effect and robustness, and we find that the exponential time-weighted method is better than the linear time-weighted method in capturing time information.     

银行定期存款客户预测——基于Lasso-Forest方法

从定性角度通过对数据进行描述性统计分析，给予银行营销策略建议。使用Lasso-Forest、Logistic、决策树及SVM模型分别进行建模分析，结合不平衡数据处理方法SMOTE算法，使用一系列评价指标进行模型效果评估，得到最优模型。所提出的Lasso-Forest组合模型具有比上述其他模型更精确的预测效果，识别准确率达到93%。使用提供的营销策略以及Lasso-Forest模型可以有效降低银行成本，对客户类型进行精确识别并加以针对性营销，以此达到增加银行定期存款储备的目的。