基于可信度的统计检验决策研究

针对单侧假设检验中出现的自相矛盾的决策问题,在简单分析单侧假设检验两类错误具体形式的基础上,给出了检验决策可信度的概念及其计算公式,并提出了用决策可信度来判断单侧检验原假设及其结论是否有效的方法.实例表明,方法是可行的,有效的.     

关于单侧检验拒绝域的证明及假设检验的概率实质

根据假设检验的基本思想 ,阐明了“检验规则”的实质 ;根据小概率原理 ,完善了对单总体参数单侧检验拒绝域的理论证明 ;根据假设检验中的参数是一个未知的常数而不是一个变量的观点 ,揭示了单侧检验的概率实质 .同时 ,还提出了单侧检验中的两个易被忽视的问题及其解决方法 .最后 ,对假设检验中的一些基本概念给出了几点简要的评注 .     

关于区间估计和假设检验的一点注记

给出了当枢轴量和检验统计量的分布密度为单调函数时,寻找最优置信区间方法,并说明了在此条件下进行假设检验选择单侧拒绝域的合理性。     

负相伴样本情形线性指数分布参数的经验Bayes检验问题

讨论了负相伴样本情形线性指数分布参数的经验Bayes(EB)单侧检验问题.利用概率密度函数的核估计构造了参数的经验Bayes单侧检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性并获得了其收敛速度.最后给出一个有关主要结果的例子.     

结构方程模型简化方法及在人机行为研究中的应用

为解决研究中结构方程模型过度复杂的问题,提出一种简化方法.分析了多维测量模型直接引入整体模型的局限性,对高阶验证性因子分析方法和项目组合法在模型简化中的适用性进行了分析,提出了首先检验简化必要性再使用高阶验证性因子分析方法和项目组合法对整体模型进行简化的两阶段方法.以电子学习系统持续使用行为的研究数据为例对该简化方法的有效性进行检验,简化前后拟合数据的对比分析表明该方法可以显著简化整体模型并获得理想的拟合优度.     

单侧检验中的零假设应当“反设”

本文说明了在单侧检验中的零假设应当根据有关的样本数字特征(如(?),S~2等)而进行反设。     

广义Pareto分布参数的经验Bayes检验问题

讨论了独立同分布样本情形广义Pareto分布参数的经验Bayes单侧检验问题,利用核密度函数的核估计构造了参数的经验Bayes检验函数,并在一定的条件下,证明了此经验Bayes检验函数的渐近最优性,获得了其收敛速度.     

一类离散型单参数指数族参数的双侧的经验Bayes检验问题

一类一维离散型单参数指数族参数的单侧的经验Bayes(EB)检验问题已有研究,但关于这类分布族的双边的EB检验问题尚无结果,本文研究这一问题,本文构造了参数的EB检验的判决函数,并且获得了它的渐近最优性和收敛速度。在文末给出定理说明了在一些情形下,加上适当的条件,精确的收敛速度可以达到n~(-1)。     

多元广义泊松分布的参数估计与诊断

广义泊松分布是普通泊松分布的自然推广,克服均值与方差相等的局限性.在计数数据中,常常会有多变量的情形,比如保险保单定价.因此文章考虑多元广义泊松分布的参数估计和假设检验问题,针对共协方差多元广义泊松模型提出两种参数估计的方法,矩估计方法和极大似然估计方法,并比较两种方法的优劣性.文章就多元广义泊松分布的假设检验问题,主要探讨了其退化检验及独立性检验,由于参数及变量较多,运用似然比检验方法构造服从卡方分布的检验统计量.最后,运用多元广义泊松理论分析不同地区森林发生火灾的次数,首先用文中提到的检验方法诊断数据是否可以用多元广义泊松分布,其次进行参数估计及实际问题的分析解释.     

Pareto分布参数的经验Bayes检验的收敛速度:NA样本情形

本文讨论了NA(negativeassociation)样本情形Pareto分布参数的经验Bayes(EB)单侧和双侧检验问题.利用概率密度函数的核估计构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性并获得了其收敛速度.     

The unilateral backward shift is w-quasisubscalar

In [Ko 2] we extend Putinar's theorem to every operator on a finite dimensional space by generalizing Putinar's techniques. Using these techniques, we construct a functional model for the unilateral backward shift. We show, in particular, that the unilateral backward shift is w-quasisubscalar. As a corollary we prove that every strict contraction is w-subscalar, i.e., is similar to the restriction to an invariant subspace of a w-scalar operator.Research partially supported by GARC.     

Inference for Spatial Autoregressive Models with Infinite Variance Noises

A self-weighted quantile procedure is proposed to study the inference for a spatial unilateral autoregressive model with independent and identically distributed innovations belonging to the domain of attraction of a stable law with index of stability α, α ∈ (0, 2]. It is shown that when the model is stationary, the self-weighted quantile estimate of the parameter has a closed form and converges to a normal limiting distribution, which avoids the difficulty of Roknossadati and Zarepour (2010) in deriving their limiting distribution for an M-estimate. On the contrary, we show that when the model is not stationary, the proposed estimates have the same limiting distributions as those of Roknossadati and Zarepour. Furthermore, a Wald test statistic is proposed to consider the test for a linear restriction on the parameter, and it is shown that under a local alternative, the Wald statistic has a non-central chisquared distribution. Simulations and a real data example are also reported to assess the performance of the proposed method.     

Existence and uniqueness of positive solutions for the Neumann p-Laplacian

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory reaction which satisfies only a unilateral growth restriction. Using the principal eigenvalue of an eigenvalue problem involving the Neumann p-Laplacian plus an indefinite potential, we produce necessary and sufficient conditions for the existence and uniqueness of positive smooth solutions.     

Shift-type invariant subspaces of contractions

Using the Sz.-Nagy-Foias functional model it was shown in [L. Kérchy, Injection of unilateral shifts into contractions with non-vanishing unitary asymptotes, Acta Sci. Math. (Szeged) 61 (1995) 443-476] that under certain conditions on a contraction T the natural embedding of a Hardy space of vector-valued functions into the corresponding L² space can be factored into the product of two transformations, intertwining T with a unilateral shift and with an absolutely continuous unitary operator, respectively. The norm estimates in the Factorization Theorem of this paper are sharpened to their best possible form by essential improvements in the proof. As a consequence we obtain that if the residual set of a contraction covers the whole unit circle then those invariant subspaces, where the restriction is similar to the unilateral shift with a similarity constant arbitrarily close to 1, span the whole space. Furthermore, the hyperinvariant subspace problem for asymptotically non-vanishing contractions is reduced to these special circumstances.     

相空间中单面非Chataev型非完整系统的Lie对称性与守恒量

研究相空间中单面非Ｃｈｅｔａｅｖ型非完整系统的Ｌｉｅ对称性与守恒量．首先根据微分方程在无限小变换下的不变性建立Ｌｉｅ对称性所满足的确定方程和限制方程,给出结构方程和守恒量;其次讨论系统的Ｌｉｅ对称性逆问题;最后举一实例说明结果的应用．     

Modelling of unilateral constraints using power-based restriction functions within Lagrangian mechanics

The consideration of unilateral contacts within multi-body systems is a common but also difficult task. Established modelling approaches such as the rigid body theory or the Hertzian contact are suitable for single-body systems but show serious problems with increasing system complexity. Indeed, there are different approaches to extend the existing models to multi-body systems, but with a growing number of contacts and the consideration of tangential friction, those enhancements are hardly applicable, showing numeric problems or becoming unmanageable. Thus, to overcome these limitations, a new modelling approach for unilateral contacts defined by power-based restriction functions is proposed in this contribution. The proposed contact model is based on continuous functions, making it numerically robust as well as applicable within Lagrangian mechanics. The approach is easily applicable and even remains manageable for multiple contacts since each constraint can be independently adapted by four physical parameters. The simple applicability and generalizability of the approach is demonstrated by several examples.     

正态总体均值与标准差比在序约束下的广义p值检验

本文利用广义$p$\,-值和U-I检验法研究了多个正态总体均值与标准差比在简单半序和树序约束下的检验问题. 提出了广义检验变量, 得到了多个正态总体均值与标准差比在简单半序和树序约束下检验问题的广义$p$\,-值. 同时运用Monte Carlo方法给出了模拟结果.     

假设检验中p值的灵活运用

给出假设检验中p值的定义以及双边检验p值与单边检验p值的关系,介绍了利用p值将三种检验同时进行的方法及意义,最后给出应用实例.     

序约束下多元正态均值的检验问题

设有k组均值有简单半序约束,协方差阵未知的p维正态分布．Sasabuchi等在2003年研究了均值是否相等的检验问题．考虑到似然比检验统计量的临界点难以获得,以致于它不容易实施,Sasabuchi提出了一个检验方法．称为Sasabuchi检验．Sasabuchi检验的一个不足之处在于,它并不优于经典的MANOVA检验．作者提出了一个新的检验方法,它比Sasabuchi检验有一致优的势,而且形式更为简单．通过模拟发现这个检验方法还优势于MANOVA．最后导出了这个检验统计量的渐近零分布．