The sliced inverse regression algorithm as a maximum likelihood procedure

It is shown that the sliced inverse regression procedure proposed by Li corresponds to the maximum likelihood estimate where the observations in each slice are samples of multivariate normal distributions with means in an affine manifold.     

Sparse subspace linear discriminant analysis

We study high dimensional multigroup classification from a sparse subspace estimation perspective, unifying the linear discriminant analysis (LDA) with other recent developments in high dimensional multivariate analysis using similar tools, such as penalization method. We develop two two-stage sparse LDA models, where in the first stage, convex relaxation is used to convert two classical formulations of LDA to semidefinite programs, and furthermore subspace perspective allows for straightforward regularization and estimation. After the initial convex relaxation, we use a refinement stage to improve the accuracy. For the first model, a penalized quadratic program with group lasso penalty is used for refinement, whereas a sparse version of the power method is used for the second model. We carefully examine the theoretical properties of both methods, alongside with simulations and real data analysis.     

Estimation of the limit variance for sums under a new weak dependence condition

We prove a self-normalized central limit theorem for a mixing class of processes introduced in Kacem M, Loisel S, Maume-Deschamps V. [Some mixing properties of conditionally independent processes. Commun Statist Theory Methods. 2016;45:1241–1259]. This class is larger than more classical strongly mixing processes and thus our result is more general than [Peligrad M, Shao QM. Estimation of the variance of partial sums for ρ-mixing random variables. J Multivar Anal. 1995;52:140–157; Shi S. Estimation of the variance for strongly mixing sequences. Appl Math J Chinese Univ. 2000;15(1):45–54] ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.     

Dependent Lindeberg central limit theorem for the fidis of empirical processes of cluster functionals

Drees H. and Rootzén H. [Limit theorems for empirical processes of cluster functionals (EPCF). Ann Stat. 2010;38(4):2145–2186] have proven central limit theorems (CLTs) for EPCF built from β-mixing processes. However, this family of β-mixing processes is quite restrictive. We expand some of those results, for the finite-dimensional marginal distributions (fidis), to a more general dependent processes family, known as weakly dependent processes in the sense of Doukhan P. and Louhichi S. [A new weak dependence condition and applications to moment inequalities. Stoch. Proc. Appl. 1999;84:313–342]. In this context, the CLT for the fidis of EPCF is sufficient in some applications. For instance, we prove the convergence without mixing conditions of the extremogram estimator, including a small example with simulation of the extremogram of a weakly dependent random process but nonmixing, in order to confirm the efficacy of our result.     

Sufficient dimension reduction via distance covariance with multivariate responses

In this article, we propose a new method for sufficient dimension reduction when both response and predictor are vectors. The new method, using distance covariance, keeps the model-free advantage, and can fully recover the central subspace even when many predictors are discrete. We then extend this method to the dual central subspace, including a special case of canonical correlation analysis. We illustrated estimators through extensive simulations and real datasets, and compared to some existing methods, showing that our estimators are competitive and robust.     

从圈层结构理论看历代政治实体的性质

本文首先阐明历史政治地理圈层结构理论的基本点,即在多民族国家一般可分为中心区和边缘区,中心区又可分为直辖区、普通区两个类型的基本圈层,可以统视之为直接行政区;边缘区可分为自治区、统领区两个类型的基本圈层,可统视之为间接行政区。然后分析中国历代政治实体的性质,将其分别归入直辖都畿区、普通经制区、羁縻自治区、藩属统领区等子圈层,认为它们与《禹贡》所反映的理想化的分封制和贡赋关系的五服圈层大体上是可以对应的。最后指出:具备一定的境域,以及多民族国家这两个要素,是圈层结构产生的必要条件,而多轨行政正是适应多民族国家国情的必然选择,是历代统治者经历几千年政治实践总结出的宝贵经验。     

中共八大前后中央与地方分权的两条思路探析

中国是一个地区发展不平衡的多民族的发展中大国,中央与地方如何分权既是一个重大的理论问题,也是一个切实的实践问题。社会主义改造基本完成后,为了改变中央高度集权的管理体制,中央开始向地方分权,并在实践中形成了渐进式分权和激进式分权两种方式,各自取得了不同的成果,这为今天处理中央与地方分权问题提供了历史的经验教训。     

中心城市首位度对区域经济协调发展的影响研究——基于中国19个城市群的分析

在2019年8月的中央财经委第五次会议上强调中心城市和城市群正在成为承载发展要素的主要空间形式，新形势下要促进区域协调发展，在发展中营造平衡。目前各地区以经济发展为核心目标所展开的城市首位度提升、强化中心城市作用的区域经济发展导向，究竟是会导致城中心城市形成对周边地区的虹吸效应，劣化区域的协调发展，还是会形成更强的龙头带动作用，扩大其辐射扩散范围，缩小地区内部的发展差距?研究针对性分析我国现阶段重要的空间形态——城市群，其中心城市首位度变化对区域整体经济增长及协调发展的影响。在理论层面，研究基于区域非均衡发展理论、城市最优规模倒U型模型对中心城市的集聚与扩散效应与区域协调发展的作用机制展开分析，构建形成中心城市首位度对区域经济协调发展的理论框架，分别从中心城市在集聚效应下对区域协调发展的抑制作用、中心城市在扩散效应下对区域协调发展的推进作用、中心城市不同首位度水平作用机制三个方面对中心城市首位度与区域经济发展不同阶段的变化及其内部作用机理展开分析。在实证层面，研究以中国十九大城市群为研究对象，利用2006—2017年中国十九大城市群面板数据展开固定效应分析，并通过内生性检验对模型内生性...     

在新的起点上继续推进农村改革的几点思考——纪念十一届三中全会30周年

我国农村在改革开放以来的30年间，已经发生了翻天覆地的变化，但同时也存在一些不容忽视的矛盾和问题。因此，为了继续推进农村改革发展，需要采取以下措施：继续创新农村土地制度；进一步完善农村社会保障制度；建立和完善农业保险制度；建立和完善加快农村人力资本积累的制度机制；创新农村金融制度；建立和完善保护农村资源环境的制度机制。