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本文在文[3]的基础上,研究了模糊事件的条件λ─独立性的有关问题,给出了两个模糊事件条件λ─独立的充要条件,推广了概率论中的相应结果。 相似文献
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随机变量的独立性在概率论中有着十分重要的意义.本文给出了离散型随机变量与离散型随机向量相互独立的概念,条件独立的概念,以及几种独立性的相互关系. 相似文献
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在误差项独立同分布的条件下,本文讨论了条件自回归极差模型条件解和无条件解的渐近性质.利用随机游动的极限性质得到了条件解收敛于无条件解的充分条件,任意阶矩有限的充要条件以及外生变量与内生变量持续性的充要条件.所得到的结论适用于已得到应用的平稳条件自回归极差模型,也适用于包含单位根的模型和满足条件的其他类型的非平稳过程,为模型的统计推断提供了理论基础. 相似文献
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克服线性回归模型中设计矩阵的复共线性,主要有三种方法追加数据自变量选择和非量小二乘法,本文研究追加数据在减少条件数中的作用,我们的研究表明,在可能情况下适当地选择追加数据,设计矩阵的条件指数可以被减少。我们用在回归最优设计中广泛初研Gaylor-Merrill数据说明了本文理论结果的实用意义。 相似文献
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连续随机变量的随机独立性与回归独立性 总被引:1,自引:0,他引:1
陈秋华 《数学的实践与认识》2004,34(2):104-110
回归独立性是指给定随机变量 X时 ,随机变量 Y的条件期望 E( Y|X)不依赖于 X.前人讨论了离散型随机变量回归独立性与随机独立性的关系 ,得到了二者等价的充分必要条件 .对连续型随机变量的情形加以讨论 ,获到了二者等价的几个充分必要条件 ,并说明在统计分析中的应用 . 相似文献
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ACharacterizationofExponentialDistributionsthroughConditionalIndependence¥HuangRenyan;ShouJilun(DepartmentofEconomy,XinyangTe... 相似文献
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George G. Roussas 《随机分析与应用》2013,31(6):1274-1309
Abstract This is a follow-up to a recent article by Prakasa Rao [15] on conditional independence, conditional mixing and conditional association. The purpose of this article is to derive rigorously some results following from conditioning. To this end, a brief review is presented of the concepts of conditional independence of events, classes of events, and random variables, followed by a conditional version of a factorization theorem, as well as a first installment of some basic results. Next, the concepts of conditional covariance and variance are introduced, and a second installment of basic results follows. Furthermore, a certain representation of the covariance is established in detail, followed by a conditional version of it, as well as a generalization. The concept of the conditional characteristic function is also recalled, and a certain inequality is established. Finally, the concept of conditional positive (negative) quadrant dependence, as well as that of conditional positive (negative) association are introduced. The article concludes with the derivation of the conditional versions of some known results, regarding positive (negative) association. This is done anticipating that conditional association (and also conditional mixing) will prove to be of significant applicability. 相似文献
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《Journal of computational and graphical statistics》2013,22(3):507-525
Residual-based shadings for enhancing mosaic and association plots to visualize independence models for contingency tables are extended in two directions: (a) perceptually uniform Hue-Chroma-Luminance (HCL) colors are used and (b) the result of an associated significance test is coded by the appearance of color in the visualization. For obtaining (a), a general strategy for deriving diverging palettes in the perceptually based HCL space is suggested. As for (b), cutoffs that control the appearance of color are computed in a data-driven way based on the conditional permutation distribution of maximum-type test statistics. The shadings are first established for the case of independence in two-way tables and then extended to more general independence models for multiway tables, including in particular conditional independence models. 相似文献
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ACharacterizationofGeometricDistributionsThroughConditionalIndependence黄任燕ACharacterizationofGeometricDistributionsThroughCon... 相似文献
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随机事件的独立性、随机变量的独立性是概率统计中的重要概念,不少学者都在这方面有所讨论.本文作者讨论了三维连续型随机变量(X,Y,Z)中三个分量X,Y,Z的相互独立性、条件独立性,得到三个引理.利用条件期望及三个引理作者给出了三变量相互独立的两个充要条件. 相似文献
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Bayesian networks (BNs) have attained widespread use in data analysis and decision making. Well-studied topics include efficient inference, evidence propagation, parameter learning from data for complete and incomplete data scenarios, expert elicitation for calibrating BN probabilities, and structure learning. It is common for the researcher to assume the structure of the BN or to glean the structure from expert elicitation or domain knowledge. In this scenario, the model may be calibrated through learning the parameters from relevant data. There is a lack of work on model diagnostics for fitted BNs; this is the contribution of this article. We key on the definition of (conditional) independence to develop a graphical diagnostic that indicates whether the conditional independence assumptions imposed, when one assumes the structure of the BN, are supported by the data. We develop the approach theoretically and describe a Monte Carlo method to generate uncertainty measures for the consistency of the data with conditional independence assumptions under the model structure. We describe how this theoretical information and the data are presented in a graphical diagnostic tool. We demonstrate the approach through data simulated from BNs under different conditional independence assumptions. We also apply the diagnostic to a real-world dataset. The results presented in this article show that this approach is most feasible for smaller BNs—this is not peculiar to the proposed diagnostic graphic, but rather is related to the general difficulty of combining large BNs with data in any manner (such as through parameter estimation). It is the authors’ hope that this article helps highlight the need for more research into BN model diagnostics. This article has supplementary materials online. 相似文献
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Anatole Beck 《Probability Theory and Related Fields》1976,33(4):253-267