On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and Its Applications

Abstract

In this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the paper generalize and improve the corresponding ones of Wang et al. (2014 Wang, X. J., X. Deng, L. L. Zheng, and S. H. Hu. 2014. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. A Journal of Theoretical and Applied Statistics 48(4):834–50. [Google Scholar]b) and Shen, Xue, and Wang (2017 Shen, A., M. Xue, and W. Wang. 2017. Complete convergence for weighted sums of extended negatively dependent random variables. Communications in Statistics – Theory and Methods 46(3):1433–44.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

极大平坦模与极大平坦维数

给出极大平坦模的定义,研究极大平坦模的性质,得到极大平坦模与平坦模、极大内射模之间的关系,并利用极大平坦维数刻画环。     

半质环的极大零化左理想

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Sylow子群全是m-正规的有限群

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Any Maximal Planar Graph with Only One Separating Triangle is Hamiltonian

A graph is hamiltonian if it has a hamiltonian cycle. It is well-known that Tutte proved that any 4-connected planar graph is hamiltonian. It is also well-known that the problem of determining whether a 3-connected planar graph is hamiltonian is NP-complete. In particular, Chvátal and Wigderson had independently shown that the problem of determining whether a maximal planar graph is hamiltonian is NP-complete. A classical theorem of Whitney says that any maximal planar graph with no separating triangles is hamiltonian, where a separating triangle is a triangle whose removal separates the graph. Note that if a planar graph has separating triangles, then it can not be 4-connected and therefore Tutte's result can not be applied. In this paper, we shall prove that any maximal planar graph with only one separating triangle is still hamiltonian.     

最大极在集是渗透及最大极小集是理想

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Optimum invariant tests for random manova models

Consider the canonical-form MANOVA setup with X: n × p = (+ E, X_i n_i × p, i = 1, 2, 3, M_i: n_i × p, i = 1, 2, n₁ + n₂ + n₃) p, where E is a normally distributed error matrix with mean zero and dispersion I_n (> 0 (positive definite). Assume (in contrast with the usual case) that M₁i is normal with mean zero and dispersion I_n1) and M₂2 is either fixed or random normal with mean zero and different dispersion matrix I_n2 (being unknown. It is also assumed that M₁ E, and M₂ (if random) are all independent. For testing H₀) = 0 versus H₁: (> 0, it is shown that when either n₂ = 0 or M₂ is fixed if n₂ > 0, the trace test of Pillai (1955) is uniformly most powerful invariant (UMPI) if min(n₁, p)= 1 and locally best invariant (LBI) if min(n₁ p) > 1 underthe action of the full linear group Gl (p). When p > 1, the LBI test is also derived under a somewhat smaller group G_T(p) of p × p lower triangular matrices with positive diagonal elements. However, such results do not hold if n₂ > 0 and M₂ is random. The null, nonnull, and optimality robustness of Pillai's trace test under Gl(p) for suitable deviations from normality is pointed out.     

细胞图像分割的新方法

细胞图像分割是细胞图像识别过程中最困难也是最重要的步骤之一。本文针对临床使用的宫颈巴氏染色涂片细胞图像的特点,提出了二种新方法:自适应窗和去粘连法。在自适应窗内只有单个细胞存在,然后在窗内采用最大方差阀值法对该细胞进行分割;去粘连法避免了通常使用的腐蚀、膨胀次数难以确定的缺点,使粘连的细胞互相分离。经过病理学家对1100个细胞的测试,证明这二个方法对提高分割效果很有效。     

社会化小农：解释当今农户的一种视角

农户是认识农业、农村、农民的钥匙,是理解和分析小农社会的基础。理论匮乏和现实需求呼唤对当今中国农户进行“再认识”,并以此为基点建构分析框架。从经营规模看,中国农民本质上仍然属于小农,但已被卷入或融入到一个高度开放的社会化体系中间,社会化水平之高史无前例。传统的经典小农学派已难以充分解释现代农民的动机与行为模式,需要建构新的小农理论范式。当今中国农村和农民处于一个社会化程度高、经营规模相对较小,且将长期存在的“社会化小农”时期,它有别于传统小农、商品小农和理性小农。这一时期是农户内部急剧变化,农民打破思维定势、突破身份歧视、冲破地域束缚,演化成为社会化、公民化的国民体系成员,荻取国民待遇的关键时期。“社会化小农”的性质、时期、形态定位,将为政府对农民国民待遇的制度安排、农村社会化服务体系建设等政策选择提供充分的理论依据。     

奇导协方差矩阵和任意收益率分布下均值-CVaR模型的有效边界特征

本文利用现代主流风险度量技术CVaR代替方差或VaR,建立了均值-CVaR模型,在任意收益率分布下,利用无套利均衡分析的方法研究了奇异协方差矩阵情形的投资组合问题,得到了模型有效边界的本质特征,最后作为结论的直接应用和说明,我们给出了一个具体的算例分析。