The Asymptotics Stability of Solutions of Some Fourth Order Differential Equation

ＴｈｅＡｓｙｍｐｔｏｔｉｃｓＳｔａｂｉｌｉｔｙｏｆＳｏｌｕｔｉｏｎｓｏｆＳｏｍｅ　ＦｏｕｒｔｈＯｒｄｅｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎ方欣华ＴｈｅＡｓｙｍｐｔｏｔｉｃｓＳｔａｂｉｌｉｔｙｏｆＳｏｌｕｔｉｏｎｓｏｆＳｏｍｅＦｏｕｒｔｈＯｒｄｅ...     

THE GLOBAL THEOREM OF A.N.BERLINSKII

ＳｏｃａｌｔｈｅＢｅｒｌｉｎｓｋｉｔｈｅｏｒｅｍｆｏｒｐｌａｎａｒｑｕａｄｒａｔｉｃＳｙｓｔｅｍ（ＱＳ）ｉｓ：ＴｈｅｏｒｅｍＡ［１］ＳｕｐｐｏｓｅｔｈａｔａＱＳｈａｓ４ｆｉｎｉｔｅｃｒｉｔｉｃａｌｐｏｉｎｔｓ（ＣＰｓ），Ｉｆｔｈｅｑｕａｄｒｉｌａ...     

Finite Groups with only S-seminormal or Selfnormal Subgroups

Ｆｉｎｉｔｅ　Ｇｒｏｕｐｓ　ｗｉｔｈ　ｏｎｌｙ　Ｓ－ｓｅｍｉｎｏｒｍａｌ　ｏｒ　Ｓｅｌｆｎｏｒｍａｌ　ＳｕｂｇｒｏｕｐｓＦｉｎｉｔｅＧｒｏｕｐｓｗｉｔｈｏｎｌｙＳ－ｓｅｍｉｎｏｒｍａｌｏｒＳｅｌｆｎｏｒｍａｌＳｕｂｇｒｏｕｐｓ￥ＺｈａｎｇＱｉｎｈａｉ...     

The Structure of NBe—rpp Semigroups

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＡｓｅｍｉｇｒｏｕｐＳｉｓｃａｌｌｅｄａｎｒｐｐｓｅｍｉｇｒｏｕｐｉｆａｌｌｐｒｉｎｃｉｐａｌｒｉｇｈｔｉｄｅａｌｓａＳ1(ａ∈Ｓ)ｏｆＳ ,ｒｅｇａｒｄｅｄａｓａｎＳ1 ｓｙｓｔｅｍ ,ａｒｅｐｒｏｊｅｃｔｉｖｅ (ｓｅｅ,[1 ]ａｎｄ [2 ] ) .ＡｓｅｍｉｇｒｏｕｐＳｉｓａｎｒｐｐｓｅｍｉｇｒｏｕｐｉｆａｎｄｏｎｌｙｉｆｆｏｒａｌｌａ∈Ｓ ,ｔｈｅｓｅｔＭａ ={ｅ∈Ｅ Ｓ1ａ Ｓｅａｎｄ ( ｘ ,ｙ∈Ｓ1)ａｘ=ａｙ ｅｘ=ｅｙ}ｉｓｎｏｎｅｍｐｔｙ ,ｗｈｅｒｅＥ …     

Examples

Ｗｅｈａｖｅｌｅａｒｎｅｄｈｏｗｔｏｃｏｎｖｅｒｔａｓｕｂｔｒａｃｔｉｏｎｔｏａｎａｄｄｉｔｉｏｎ .Ｎｏｗｌｅｔ’ｓｔａｋｅｓｏｍｅｅｘａｍｐｌｅ.ｓ .Ｅｘａｍｐｌｅ 1　　　Ｓｉｍｐｌｉｆｙ　 - 5- 2 .Ｓｏｌｕｔｉｏｎ 1Ｕｓｅｔｈｅｓｌｉｄｅｍｏｄｅｌ.Ｓｔａｒｔａｔ - 5ａｎｄｓｌｉｄｅｄｏｗｎ 2Ｔｈｅｒｅｓｕｌｔｉｓ - 7.Ｓｏ - 5- 2 =- 7.Ｓｏｌｕｔｉｏｎ 2 :ＵｓｅｔｈｅＡｌｇｅｂｒａｉｃＤｅｆｉｎｉｔｉｏｎｏｆＳｕｂｔｒａｃｔｉｏｎ .- 5- 2 =- 5+- 2 =- 7(Ｉｎｓｔｅａｄｏｆｓｕｂｔｒａｃｔｉｎｇ 2…     

A Note on C-wrpp Semigroups

ＬｅｔＲｄｅｎｏｔｅＧｒｅｅｎ ｓＲ ｒｅｌａｔｉｏｎｏｎａｓｅｍｉｇｒｏｕｐＳ .ＷｅｄｅｆｉｎｅａｒｉｇｈｔｃｏｎｇｒｕｅｎｃｅＬ ｏｎＳｉｎｔｈｅｒｕｌｅ:ｆｏｒａ ,ｂ∈Ｓ ,(ａ ,ｂ) ∈Ｌ ｉｆｆｆｏｒａｌｌｘ ,ｙ∈Ｓ1,　　 (ａｘ ,ａｙ) ∈Ｒ (ｂｘ,ｂｙ) ∈Ｒ .ＡｓｅｍｉｇｒｏｕｐＳｉｓｓａｉｄｔｏｂｅａＣ ｗｒｐｐｓｅｍｉｇｒｏｕｐｉｆａｌｌｉｄｅｍｐｏｔｅｎｔｓｏｆＳａｒｅｃｅｎｔｒａｌｉｎＳａｎｄｅａｃｈＬ ｃｌａｓｓｏｆＳｃｏｎｔａｉｎｓａｎｉｄｅｍｐｏｔｅｎｔ(ｓｅｅ [1 ] ) .　Ｔｈｅｐ…     

The Limit Distribution of Some PP CM Statistics with Enough High Dimensions and Large Sample Size

ＴｈｅＬｉｍｉｔＤｉｓｔｒｉｂｕｔｉｏｎｏｆＳｏｍｅＰＰＣＭＳｔａｔｉｓｔｉｃｓｗｉｔｈＥｎｏｕｇｈＨｉｇｈＤｉｍｅｎｓｉｏｎｓａｎｄＬａｒｇｅＳａｍｐｌｅＳｉｚｅＣｈｅｎｇＰｉｎｇ（成平）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ａｃａ...     

三面角的棱面角的计算公式

定理　在三面角Ｓ—Ａ1 Ｂ1 Ｃ1 中 ,三个面角∠Ｃ1 ＳＢ1 =α ,∠Ａ1 ＳＣ1 =β ,∠Ａ1 ＳＢ1 =γ ,且棱ＳＡ1 和平面Ｃ1 ＳＢ1 所成棱面角为θ1 ,棱ＳＢ1 和平面Ａ1 ＳＣ1 所成棱面角为θ2 ,棱ＳＣ1 和平面Ａ1 ＳＢ1 所成棱面角为θ3,则ｃｏｓθ1 =ｃｏｓ2 β ｃｏｓ2 γ- 2ｃｏｓαｃｏｓβｃｏｓγｓｉｎαｃｏｓθ2 =ｃｏｓ2 γ ｃｏｓ2 α- 2ｃｏｓαｃｏｓβｃｏｓγｓｉｎβｃｏｓθ3=ｃｏｓ2 α ｃｏｓ2 β- 2ｃｏｓαｃｏｓβｃｏｓγｓｉｎγ(三面角的棱面角余弦公式 )证明　如图 .在ＳＡ1 上取一点Ｐ ,作ＰＱ⊥平面Ｂ1 ＳＣ1 …     

A Class of Planar Surfaces in Surface×I

Ｗｅｒｅｓｔｒｉｃｔｏｕｒｃｏｎｓｉｄｅｒａｔｉｏｎｔｏｏｒｉｅｎｔａｂｌｅａｎｄｃｏｍｐａｃｔｃａｔｅｇｏｒｙ .Ｆｏｒｄｅｆｉｎｉｔｉｏｎｓａｎｄｔｅｒｍｉｎｏｌｏｇｙ ,ｓｅｅｆｏｒｅｘａｍｐｌｅ ,[1 ]ａｎｄ [2 ].　ＬｅｔＳｂｅａｃｌｏｓｅｄｏｒｉｅｎｔａｂｌｅｓｕｒｆａｃｅｗｉｔｈｐｏｓｉｔｉｖｅｇｅｎｕｓ .Ｉｎｔｈｉｓｐａｐｅｒ ,ＭａｌｗａｙｓｄｅｎｏｔｅｓＳ×Ｉ ,ａｎｄＳ0 =Ｓ× 0 ,Ｓ1=Ｓ× 1 .ＡｎａｎｎｕｌｕｓＡｉｎＭｗｉｔｈｉｔｓｔｗｏｂｏｕｎｄａｒｉｅｓｌｙｉｎｇｉｎＳ0ａｎｄＳ1ｒ…     

Some Properties of Sums of Independent Random Sets

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＳｕｍｓｏｆＩｎｄｅｐｅｎｄｅｎｔＲａｎｄｏｍＳｅｔｓ＊）ＷａｎｇＲｏｎｇｍｉｎｇ（汪荣明）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２０００...     

Asymptotic Normality of a Combined Regression Estimator

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.     

Panel模型中常见估计的比较

本文研究了Panel模型中回归系数常见估计的比较问题,给出了在Pitman准则,协方差阵准则和广义均方误差准则下最小二乘估计,Within估计,Between估计及两步估计之间的优良性比较结果.特别地,本文证明了在Pitman准则下最小二乘估计一致地优于Between估计.     

基于奇异值分解的岭型回归(英文)

本文基于设计阵的奇异值分解(SVD),从LS估计出发,应用岭回归估计方法,构造了回归系数的一个新的有偏估计,称为基于SVD的岭型回归估计,简称RRSVD估计,讨论了其性质和偏参数的选取问题,得到了许多重要结论.计算结果表明,在设计阵呈病态时,RRS善岭回归估计.     

Kernel estimators of the ROC Curve with censored data

Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed.     

Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Typ e-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include...     

SOME RESULTS ON ESTIMATION OF THE TAIL INDEX OF A DISTRIBUTION

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＳｕｐｐｏｓｅｔｈａｔＦｉｓａｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎｓｕｃｈｔｈａｔ,ｆｏｒａｎｙｘ＞０,ｌｉｍｔ→∞１－Ｆ（ｔｘ）１－Ｆ（ｔ）＝ｘ－１γ,γ＞０．（１．１）ＷｅｃａｌγｔｈｅｔａｉｌｉｎｄｅｘｏｆＦ．...     

随机变量二次型的协方差在混合效应模型中的应用

本文提出方差分量ANOVA估计的一种改进方法, 证明了对于一般的方差分量模型, 只要方差分量的ANOVA估计存在就可以通过此方法给出其改进形式, 并且在均方误差意义下优于ANOVA估计. 特别地, 对于单向分类随机效应模型, Kelly和Mathew^[1]对ANOVA估计的改进就是我们提出的改进方法的特殊形式, 这也给出了此类改进估计在均方误差意义下优于ANOVA估计的另一种合理的解释. 同时, 本文又将此思想应用到对谱分解估计的改进上. 本文应用协方差的简单性质证明了对带有一个随机效应的方差分量模型, 当随机效应的协方差阵只有一个非零特征值时, 随机效应方差分量谱分解估计在均方误差意义下总是优于ANOVA估计. 本文最后将第三节的结论推广到广义谱分解估计下, 同时给出广义谱分解估计待定系数的一个合理的取值.     

Nonparametric estimators of the survival function with twice censored data

Patilea and Rolin (Ann Stat 34(2):925–938, 2006) proposed a product-limit estimator of the survival function for twice censored data. In this article, based on a modified self-consistent (MSC) approach, we propose an alternative estimator, the MSC estimator. The asymptotic properties of the MSC estimator are derived. A simulation study is conducted to compare the performance between the two estimators. Simulation results indicate that the MSC estimator outperforms the product-limit estimator and its advantage over the product-limit estimator can be very significant when right censoring is heavy.     

平衡数据结构下ANOVA 估计和SD 估计的比较

在线性混合效应模型下, 方差分析(ANOVA) 估计和谱分解(SD) 估计对构造精确检验和广义P-值枢轴量起着非常重要的作用. 尽管这两估计分别基于不同的方法, 但它们共享许多类似的优点, 如无偏性和有精确的表达式等. 本文借助于已得到的协方差阵的谱分解结果, 揭示了平衡数据一般线性混合效应模型下ANOVA 估计与SD 估计的关系, 并分别针对协方差阵两种结构: 套结构和多项分类随机效应结构, 给出了ANOVA 估计与SD 估计等价的充分必要条件.     

Simultaneous estimation of Poisson means

In the simultaneous estimation of means from independent Poisson distributions, an estimator is developed which incorporates a prior mean and variance for each Poisson mean estimated. This estimator possesses substantially smaller risk than the usual estimator in a region of the parameter space and seems superior to other estimators proposed to estimate p Poisson means. It is indicated through two asymptotic results that, unlike the conjugate Bayes estimator, the risk of the estimator does not greatly exceed the risk of the usual estimator outside of the region of risk improvement.