Rate of uniform consistency for nonparametric estimates with functional variables

In this paper we investigate nonparametric estimation of some functionals of the conditional distribution of a scalar response variable Y given a random variable X taking values in a semi-metric space. These functionals include the regression function, the conditional cumulative distribution, the conditional density and some other ones. The literature on nonparametric functional statistics is only concerning pointwise consistency results, and our main aim is to prove the uniform almost complete convergence (with rate) of the kernel estimators of these nonparametric models. Unlike in standard multivariate cases, the gap between pointwise and uniform results is not immediate. So, suitable topological considerations are needed, implying changes in the rates of convergence which are quantified by entropy considerations. These theoretical uniform consistency results are (or will be) key tools for many further developments in functional data analysis.     

On Markov-switching periodic ARMA models

In this work, we propose a generalization of the classical Markov-switching ARMA models to the periodic time-varying case. Specifically, we propose a Markov-switching periodic ARMA (MS-PARMA) model. In addition of capturing regime switching often encountered during the study of many economic time series, this new model also captures the periodicity feature in the autocorrelation structure. We first provide some probabilistic properties of this class of models, namely the strict periodic stationarity and the existence of higher-order moments. We thus propose a procedure for computing the autocovariance function where we show that the autocovariances of the MS-PARMA model satisfy a system of equations similar to the PARMA Yule–Walker equations. We propose also an easily implemented algorithm which can be used to obtain parameter estimates for the MS-PARMA model. Finally, a simulation study of the performance of the proposed estimation method is provided.     

NEHARI技巧在HAMILTON系统的极小周期解的存在性问题中的应用

利用关于约束极值的Nehari技巧和完备Finsler流形上满足Palais-Smale条件的下有界连续可微泛函存在极小值点的定理,研究了非凸二次和超二次二阶Hamilton系统的极小周期解的存在性。     

二阶奇异p-Hamilton系统的周期解

使用圈空间上的畴数理论在p-强力条件下证明了二阶奇异p-Hamilton系统无究多周期解的存在性，推广了p=2时一些已有的结果。     

跳出"周期率"--论中国共产党的反腐败斗争

"历览前贤国与家,成由勤俭败由奢",这几乎成了一个"周期率".中国共产党自诞生之日起就为跳出这一"周期率"展开了不懈的斗争.中国共产党80年的历史已充分证明,并且还将继续证明,中国共产党完全能够跳出这一"周期率".     

自然科学发展的周期规律

自然科学发展周期规律是描述科学范式产生、发展、完善的历史演化过程的规律,可划分为四个阶段:初创期、构造期、发展期和成熟期。初创期是科学家怀疑和批判旧科学范式,提出新概念、新定律的时期。构造期是科学大师确立基本原理,提出基本图景,做出基本推论,创建新科学范式的时期。发展期是大批自然科学家在实践中检验、修正、丰富、发展和接受新科学范式的时期。成熟期是新科学范式日臻完善,更加新的科学范式逐渐萌发的交会期。     

农地产权制度改革与农地流转响应:预期偏离与逻辑阐释

农地所有权归属集体以来,产权拆分及农民产权份额的扩大和强化是产权制度改革的主要思路。然而,理论上有效的农地产权制度改革,却在农地流转的推动成效方面呈现时段上的异质性。随着时间的演进,改革对农地流转的正面作用渐衰,甚至表现出对农地流转的抑制。为解释理论与现实的偏差,聚焦改革路径的形成逻辑,重点阐述了改革历程及改革对农地配置的影响成效,提炼出改革成效不足的系统性成因。研究认为,产权理论的引入为确定改革方向提供了理论依据,过去的改革经验为决策层延续产权赋予式改革提升了信心,规模经营路线的确立加强了坚持并推进改革的必要性和紧迫性。改革开放以后,农地产权制度朝着扩大集体成员权能的方向不断推进,却在现阶段表现出抑制农地流转并冲击农地承包权稳定性的负面影响。〖JP2〗对此,构建了涵盖政策有效性、农地多功能性以及中央决策层认知调整在内的解释框架。认为在追求现代农业发展的目标导向下,扩大集体成员的土地权能并不可取,增强农村基本经营制度中“统”的作用并以社会保障弥补农户对农地的非生产性寄托是关键。     

Stepanov-like almost automorphic solutions for stochastic differential equations with Lévy noise

In this paper, we introduce a new concept of Poisson Stepanov-like almost automorphy (or Poisson S²-almost automorphy). Under some suitable conditions on the coefficients, we establish the existence and uniqueness of Stepanov-like almost automorphic mild solution to a class of semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solution. Finally, we give an example to illustrate the theoretical results obtained in this paper.     

Block bootstrap for periodic characteristics of periodically correlated time series

This research is dedicated to the study of periodic characteristics of periodically correlated time series such as seasonal means, seasonal variances and autocovariance functions. Two bootstrap methods are used: the extension of the usual Moving Block Bootstrap (EMBB) and the Generalised Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual Moving Block Bootstrap does not preserve the periodic structure contained in the data and cannot be applied for the considered problems. For the aforementioned periodic characteristics the bootstrap estimators are introduced and consistency of the EMBB in all cases is obtained. Moreover, the GSBB consistency results for seasonal variances and autocovariance function are presented. Additionally, the bootstrap consistency of both considered techniques for smooth functions of the parameters of interest is obtained. Finally, the simultaneous bootstrap confidence intervals are constructed. A simulation study to compare their actual coverage probabilities is provided. A real data example is presented.     

On Mixture Periodic Vector Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007 Fong, P.W., Li, W.K., Yau, C.W., Wong, C.S. (2007). On a mixture vector autoregressive model. The Canadian Journal of Statistics 35:135–150.[Crossref], [Web of Science ®] , [Google Scholar]). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVAR_S(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.