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asymptotically OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES

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Chinese Annals of Mathematics,Series B 1989年第1期10卷 94-104页

作者：韦来生 Departmen of Mathematicst University of Science and Technology of China Hefei Anhui China

Consider the two-sided truncation distrbution families written in the formf（x,θ）dx=w（θ1, θ2）h（x）I[θ1,θ2]（x）dx, where θ=（θ1,θ2）.T（x）=（t1（x）, t2（x））=（min（x1,…,xm）, max（x1, …,xm））is a sufficient statistic and its marginal density is denoted by f（t）dμT. The prior distribution of θ belongs to the familyF={G:∫‖θ‖2dG（θ）n （t）, by using the kernel estimation of f（t）. Under a quite general assumption imposed upon f（t） and h（x）, it is shown that φn（t） is an asymptotically optimal EBE of θ.

关键词： truncation kernel sided estimator asymptotically prior statistic constructs assumption marginal

Rosenthal's Inequalities for asymptotically Almost Negatively Associated Random Variables Under Upper Expectations

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 117-130页

作者： Ning ZHANG Yuting LAN School of Mathematics Shandong University School of Statistics and Management Shanghai University of Finance and Economics

In this paper, the authors generalize the concept of asymptotically almost negatively associated random variables from the classic probability space to the upper expectation space. Within the framework, the authors prove some different types of Rosenthal's inequalities for sub-additive expectations. Finally, the authors prove a strong law of large numbers as the application of Rosenthal's inequalities.

关键词： Upper expectations asymptotically almost negatively associated Rosenthal's inequalities Strong law of large numbers

Pseudo asymptotically Periodic Solutions for Volterra Difference Equations of Convolution Type

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 501-514页

作者： Zhinan XIA Department of Applied Mathematics Zhejiang University of Technology

In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski’s fixed point technique.

关键词： Pseudo asymptotically periodic function Volterra difference equations Contraction mapping principle Leray-Schauder alternative theorem

asymptotically　EFFICIENT　ESTIMATES　IN　A　SYSTEM　TREE

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Systems Science and Mathematical Sciences 1996年第2期9卷 157-163页

作者： DAI Ming(Department of Applied Mathematics Beijing institute of Technology, Beijing, 100081, China) 北京理工大学应用数学系北京

ＡＳＹＭＰＴＯＴＩＣＡＬＬＹＥＦＦＩＣＩＥＮＴＥＳＴＩＭＡＴＥＳＩＮＡＳＹＳＴＥＭＴＲＥＥＤＡＩＭｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓＢｅｉｊｉｎｇｉｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌ... 详细信息

ＡＳＹＭＰＴＯＴＩＣＡＬＬＹＥＦＦＩＣＩＥＮＴＥＳＴＩＭＡＴＥＳＩＮＡＳＹＳＴＥＭＴＲＥＥＤＡＩＭｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓＢｅｉｊｉｎｇｉｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｂｅｉｊｉｎｇ，１０００８...

关键词： Virtual system method (VS Method) system tree subsystem tree, asymptotically efficient.

A Class of asymptotically Optimal Sequential Tests for Composite Hypotheses'

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Science China Mathematics 1994年第11期37卷 1314-1324页

作者：陈家鼎 FredJ.Hickernell Department of Probability and Statistics Peking UniversityBeijing 100871PRC Department of Mathematics Hong Kong Baptist CollegeHong Kong

Suppose that X has density f(x,θ)=exp(θx-ψ(θ)} (with respect to some measure v),where θ∈(θ,θ),∞≤θ≤+∞.Consider the problem of testing the hypothesis θ≤θ0 against θ≥θ1 for some given θ0 and θ1 (θ<... 详细信息

关键词： sequential testing composite hypotheses asymptotically optimal stochastic process of exponential type.

MASLOV-TYPE INDEX, DEGENERATE CRITICAL POINTS, AND asymptotically LINEAR HAMILTONIAN SYSTEMS

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Science China Mathematics 1990年第12期33卷 1409-1419页

作者：龙以明 Nankai Institute of Mathematics Nankai University Tianjin 300071 PRC

This paper introduces a Maslov-type index theory for paths in the symplectic groups, especially for the degenerate paths via rotational perturbation method, therefore gives a full classification of the linear Hamiltonian systems with continuous, periodic, and symmetric coefficients. Associating this index with each periodic solution, we establish the existence of muhiple periodic solutions of asymptotically linear Hamihonian systems.

关键词： Maslov-type index degenerate critical points rotational perturbation method periodic solutions asymptotically linear Hamiltonian systems.

Asymptotic Behavior of Almost-orbits of asymptotically Nonexpansive Semigroups in Banach Spaces(Dedicated to Professor You Zhaoyong for his 60th brithday)

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工程数学学报 1991年第2期8卷 19-30页

作者： Xu Hong-KunInstitute of Applied Mathematics, East China University of Chemical Technology, Changhai 200237, China

Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. Then we show that {u(t):t ≥ 0} is almost convergent weakly to a common fixed point y of F, that isweak - lim1/tdr - y uniformly in s≥ *** implies that {u(t):t≥ 0} converges weakly to y if and onlyif u is weakly asymptotically regular, i.e lim (u(t + s) - u(t) = 0 weakly for all s≥ 0.

关键词： Almost-orbit asymptotically nonexpansive semigroup almost convergence fixed point nonexpansive retraction.

ON asymptotically MEDIAL UNBIASED ESTIMATORS IN TRVNCATED－TYPE DISTRIBUTION FAMILIES

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Systems Science and Mathematical Sciences 1995年第2期8卷 128-130,131132+133页

作者： LIANG Hua(Institute of Systems Science,Academia Sinica,Beijing 100080,China)

ＯＮＡＳＹＭＰＴＯＴＩＣＡＬＬＹＭＥＤＩＡＬＵＮＢＩＡＳＥＤＥＳＴＩＭＡＴＯＲＳＩＮＴＲＶＮＣＡＴＥＤ－ＴＹＰＥＤＩＳＴＲＩＢＵＴＩＯＮＦＡＭＩＬＩＥＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎ... 详细信息

ＯＮＡＳＹＭＰＴＯＴＩＣＡＬＬＹＭＥＤＩＡＬＵＮＢＩＡＳＥＤＥＳＴＩＭＡＴＯＲＳＩＮＴＲＶＮＣＡＴＥＤ－ＴＹＰＥＤＩＳＴＲＩＢＵＴＩＯＮＦＡＭＩＬＩＥＳＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ...

关键词： Truncated distribution asymptotically medial unbiasedness semiparametric Model

ON　THE　SMALLEST　POSSIBLE　asymptotically　EFFICIENT　VARIANCE　IN　SEMIPARAMETRIC　MODELS

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Systems Science and Mathematical Sciences 1994年第1期7卷 29-33页

作者： LIANG Hua(Institute Of Systems Science, Academia Sinica, Beliing 100080, China) 中科院系统科学所北京 100080

ＯＮＴＨＥＳＭＡＬＬＥＳＴＰＯＳＳＩＢＬＥＡＳＹＭＰＴＯＴＩＣＡＬＬＹＥＦＦＩＣＩＥＮＴＶＡＲＩＡＮＣＥＩＮＳＥＭＩＰＡＲＡＭＥＴＲＩＣＭＯＤＥＬＳ￥ＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅＯｆＳｙｓｔｅｍｓＳｃｉｅｎｃ... 详细信息

ＯＮＴＨＥＳＭＡＬＬＥＳＴＰＯＳＳＩＢＬＥＡＳＹＭＰＴＯＴＩＣＡＬＬＹＥＦＦＩＣＩＥＮＴＶＡＲＩＡＮＣＥＩＮＳＥＭＩＰＡＲＡＭＥＴＲＩＣＭＯＤＥＬＳ￥ＬＩＡＮＧＨｕａ（ＩｎｓｔｉｔｕｔｅＯｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，...

关键词： Semiparametric models the smallest possible asymptotically efficient variance.