Subsampling-extrapolation bandwidth selection in bivariate kernel density estimation

This paper focuses on bivariate kernel density estimation that bridges the gap between univariate and multivariate applications. We propose a subsampling-extrapolation bandwidth matrix selector that improves the reliability of the conventional cross-validation method. The proposed procedure combines a U-statistic expression of the mean integrated squared error and asymptotic theory, and can be used in both cases of diagonal bandwidth matrix and unconstrained bandwidth matrix. In the subsampling stage, one takes advantage of the reduced variability of estimating the bandwidth matrix at a smaller subsample size m (m < n); in the extrapolation stage, a simple linear extrapolation is used to remove the incurred bias. Simulation studies reveal that the proposed method reduces the variability of the cross-validation method by about 50% and achieves an expected integrated squared error that is up to 30% smaller than that of the benchmark cross-validation. It shows comparable or improved performance compared to other competitors across six distributions in terms of the expected integrated squared error. We prove that the components of the selected bivariate bandwidth matrix have an asymptotic multivariate normal distribution, and also present the relative rate of convergence of the proposed bandwidth selector.     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Hard thresholding regression

In this paper, we propose the hard thresholding regression (HTR) for estimating high‐dimensional sparse linear regression models. HTR uses a two‐stage convex algorithm to approximate the ?₀‐penalized regression: The first stage calculates a coarse initial estimator, and the second stage identifies the oracle estimator by borrowing information from the first one. Theoretically, the HTR estimator achieves the strong oracle property over a wide range of regularization parameters. Numerical examples and a real data example lend further support to our proposed methodology.     

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.     

Fast and approximate exhaustive variable selection for generalised linear models with APES

We present APproximated Exhaustive Search (APES), which enables fast and approximated exhaustive variable selection in Generalised Linear Models (GLMs). While exhaustive variable selection remains as the gold standard in many model selection contexts, traditional exhaustive variable selection suffers from computational feasibility issues. More precisely, there is often a high cost associated with computing maximum likelihood estimates (MLE) for all subsets of GLMs. Efficient algorithms for exhaustive searches exist for linear models, most notably the leaps‐and‐bound algorithm and, more recently, the mixed integer optimisation (MIO) algorithm. The APES method learns from observational weights in a generalised linear regression super‐model and reformulates the GLM problem as a linear regression problem. In this way, APES can approximate a true exhaustive search in the original GLM space. Where exhaustive variable selection is not computationally feasible, we propose a best‐subset search, which also closely approximates a true exhaustive search. APES is made available in both as a standalone R package as well as part of the already existing mplot package.     

基于个性化需求的产品竞争供应链结构选择

基于"制销分离"与"定制一体"两种结构选择,构建个性化产品供应链处于非竞争与竞争环境下的博弈模型,在引入一个实际案例的基础上,运用算例仿真比较分析两种运营模式下的供应链运作策略和盈利差异。结果显示：与制销分离结构相比,个性化产品供应链选择定制一体结构,有利于匹配产品个性化制造、提升产品个性化水平和市场需求、增加供应链的期望收益;个性化产品供应链选择制销分离结构时,适度的批发价格激励能够提升产品个性化水平、更好满足消费者个性化需求、改善供应链的运营绩效,分销商适度让利加大批发价格激励力度可显著促进产品个性化制造互动、提升产品个性化水平;竞争将消减个性化产品供应链的运营绩效,但选择定制一体结构可显著提升竞争力。     

不对称信息下风险投资家与风险企业家之间的委托代理问题研究

风险投资体系以多重激励和不对称信息为特征,风险投资的三方利益主体之间存在着双重委托-代理关系,有效控制代理风险是风险投资高效运作的基本前提。本文基于信息经济学原理,分析了风险投资家与风险企业家之间代理风险的成因,并从委托人的角度讨论了风险治理的原则和投资契约的构造。     

心理学对经济学的贡献

随着人类经济活动的日益丰富与多样化,以新古典理论为核心的主流经济学不断与现实经济世界产生矛盾与冲突,许多经济现象仅通过对理性人模型的量变扩张已无法解释。认知心理学的发展为经济学考察人类的经济行为提供了坚实的科学依据。被称作＂心理学的经济学＂的行为经济学,剥去了假设理性人光鲜的外衣,强调对行为的分析应以行为的真实心理形成机制为基础,不能以主观的先验假定为依据。行为经济学更适合对我国当前整体经济行为的深入研究。将个体行为纳入经济学分析体系,这对我国构建以人为本的和谐社会具有重要的现实意义。行为经济学修正了主流经济理论中＂自利人＂的假定,吸收社会心理学关于＂利他行为＂等研究成果,不仅与我国传统道德文化相吻合,对当前构建市场经济条件下社会主义核心价值体系更具借鉴意义。