LARGE DEVIATIONS FOR INFINITE DIMENSIONAL AND REVERSIBLE REACTION－DIFFUSION PROCESSES

ＬＡＲＧＥＤＥＶＩＡＴＩＯＮＳＦＯＲＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＡＮＤＲＥＶＥＲＳＩＢＬＥＲＥＡＣＴＩＯＮ－ＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＣＨＥＮＪＩＮＷＥＮ（陈金文）（ＤｅｐｅｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔ...     

A SUCCESSIVE APPROXIMATION METHOD FOR SOLVING PROBABILISTIC CONSTRAINED PROGRAMS

ＡＳＵＣＣＥＳＳＩＶＥＡＰＰＲＯＸＩＭＡＴＩＯＮＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＰＲＯＢＡＢＩＬＩＳＴＩＣＣＯＮＳＴＲＡＩＮＥＤＰＲＯＧＲＡＭＳＷＡＮＧＪＩＮＤＥ（王金德）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓ...     

ARONSON'S ESTIMATES AND CONDITIONAL DIFFUSION PROCESSES

ＡＲＯＮＳＯＮ＇ＳＥＳＴＩＭＡＴＥＳＡＮＤＣＯＮＤＩＴＩＯＮＡＬＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＱＩＡＮＺＨＯＮＧＭＩＮ（钱忠民）ＷＥＩＧＵＯＱＩＡＮＧ（魏国强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈ...     

A SUFFICIENT CONDITION FOR NON－COEXISTENCE OF ONE DIMENSIONAL MULTICOLOR CONTACT PROCESSES

ＡＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＮＯＮ－ＣＯＥＸＩＳＴＥＮＣＥＯＦＯＮＥＤＩＭＥＮＳＩＯＮＡＬＭＵＬＴＩＣＯＬＯＲＣＯＮＴＡＣＴＰＲＯＣＥＳＳＥＳＬＩＵＸＩＵＦＡＮＧ（刘秀芳）ＷＡＮＧＪＵＮ（王军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

SHAPE PRESERVING PROPERTIES AND CONVERGENCE OF UNIVARIATE MULTIQUADRIC QUASI－INTERPOLATION

ＳＨＡＰＥＰＲＥＳＥＲＶＩＮＧＰＲＯＰＥＲＴＩＥＳＡＮＤＣＯＮＶＥＲＧＥＮＣＥＯＦＵＮＩＶＡＲＩＡＴＥＭＵＬＴＩＱＵＡＤＲＩＣＱＵＡＳＩ－ＩＮＴＥＲＰＯＬＡＴＩＯＮＷｕＺＯＮＧＭＩＮ（吴宗敏）（ＤｅｐｅｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｆｕｄａ...     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

ＦＩＸＥＤＰＯＩＮＴＳＡＮＤＣＯＵＰＬＥＤＦＩＸＥＤＰＯＩＮＴＳＦＯＲＩＮＣＲＥＡＳＩＮＧＯＰＥＲＡＴＯＲＳＷＩＴＨＡＰＰＬＩＣＭＩＯＮＳＴＯＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺＨＡＮＧＳＨＩＳＨＥＮＧＡＮＤＨＵ...     

STRONG LAWS FOR α-MIXING SEQUENCE PROCESSES INDEXED BY SETS

ＳＴＲＯＮＧＬＡＷＳＦＯＲα－ＭＩＸＩＮＧＳＥＱＵＥＮＣＥＰＲＯＣＥＳＳＥＳＩＮＤＥＸＥＤＢＹＳＥＴＳ￥ＸＵＢＩＮＧＡｂｓｔｒａｃｔ：ＬｅｔＪ＝｛１，２，．．．｝ｄａｎｄｌｅｔ｛Ｘｊ，ｊ∈Ｊ｝ｂｅａｎａ－ｍｉｘｉｎｇｓｅｑｕｅｎｃｅｗｈｉｃｈｉｓｎｏ...     

MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

ＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＡＮＤＷＥＡＫＬＹＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＯＦＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧ￥ＨＵＹＵＤＡ（Ｄｅｐｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＳｈａｎｇｈａｉＪｉａｏＴｏｎ...     

SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES

ＳＭＡＬＬＰＥＲＴＵＲＢＡＴＩＯＮＣＲＡＭＥＲＭＥＴＨＯＤＳＡＮＤＭＯＤＥＲＡＴＥＤＥＶＩＡＴＩＯＮＳＦＯＲＭＡＲＫＯＶＰＲＯＣＥＳＳＥＳＧａｏＦｕｑｉｎｇ（高付清）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｍａｔｉｃｓ，ＨｕｂｅｉＵａｉｖｅｒｓｉｔｙ，Ｗｕ...     

STRONGLY ALGEBRAIC LATTICES AND CONDITIONS OF MINIMAL MAPPING PRESERVING INFS

ＳＴＲＯＮＧＬＹ ＡＬＧＥＢＲＡＩＣ ＬＡＴＴＩＣＥＳ ＡＮＤ ＣＯＮＤＩＴＩＯＮＳ ＯＦ ＭＩＮＩＭＡＬ ＭＡＰＰＩＮＧ ＰＲＥＳＥＲＶＩＮＧ ＩＮＦＳ ￥ＸＵＸＩＡＯＱＵＡＮＡｂｓｔｒａｃｔ：Ｔｈｅｔａｂｏｒｇｉｖｅｓｓｏｍｅｃｈａｒａｃｔｅｒｉ...     

Bootstrapping generalizedU-processes andV-processes and their applications in projection pursuit

In this paper, we study bootstrap approximation for generalizedU-processes (GUP) indexed by a class of functions. Under mild conditions we obtain that the asymptotic distributions of bootstrapping generalizedU-processes (BGUP) are the same as those of GUP almost surely. As a result, the asymptotic properties of bootstrap approximation for PP generalizedU-processes (BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUP and GVP.This project is supported by the National Natural Science Foundation of China and the Science Foundation of Educational Committee of Guizhou.     

EDGEWORTH EXPANSION AND BOOTSTRAP APPROXIMATION FOR THE STUDENTIZED MLE FROM RANDOMLY CENSORED EXPONENTIAL SAMPLES

In this paper,the author studies the asymptotic accuracies of the one-term Edgeworth expansions and the bootstrap approximation for the studentized MLE from randomly censored exponential population.It is shown that the Edgeworth expansions and the bootstrap approximation are asymptotically close to the exact distribution of the studentized MLE with a rate.     

随机加权U-过程的条件弱收敛

假定Ｆ是一个由函数组成的集合．在这篇文章中,我们研究了指标集Ｆ上２阶的随机加权Ｕ－过程的条件弱收敛性质,导出了Ｕ－过程的随机加权逼近．     

一类广义插值函数与广义有限元方法的后验估计

１．问题的提出具有快速振荡系数的微分方程大量出现在复合材料、多孔介质渗流等实际问题中．因为这类方程系数的激烈振荡性（受小尺度ε控制）,通常的有限元方法需花费巨大的计算工作量才能获得有意义的数值解（文［７］）,这对多维问题是无法承受的．８０年代发展起来的广义有限元法（文［１］［３］［５］）,为这类问题的解决提供了一条有效的新途径,它可在剖分步长ｈ＞＞　ε的情况下得到令人满意的数值结果．在广义有限元的理论分析中,因方程解的正则性估计通常与小尺度ε　有关,所以通常的有限元分析方法有一定的困难,目前尚未…     

An asymptotics look at the generalized inference

This paper provides an asymptotics look at the generalized inference through showing connections between the generalized inference and two widely used asymptotic methods, the bootstrap and plug-in method. A generalized bootstrap method and a generalized plug-in method are introduced. The generalized bootstrap method can not only be used to prove asymptotic frequentist properties of existing generalized confidence regions through viewing fiducial generalized pivotal quantities as generalized bootstrap variables, but also yield new confidence regions for the situations where the generalized inference is unavailable. Some examples are presented to illustrate the method. In addition, the generalized F-test (Weerahandi, 1995 [26]) can be derived by the generalized plug-in method, then its asymptotic validity is obtained.     

Edgeworth expansion for the survival function estimator in the Koziol-Green model

In the Koziol-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studentized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.     

Asymptotic Expansions of Generalized Stieltjes Transforms of Algebraically Decaying Functions

Asymptotic expansions of Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative integer powers of their variable have been exhaustively investigated by R. Wong. In this article, we extend this analysis to Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative rational powers of their variable. Distributional approach is used to derive asymptotic expansions of the Stieltjes and generalized Stieltjes transforms of this kind of functions for large values of the parameter(s) of the transformation. Error bounds are obtained at any order of the approximation for a large family of integrands. The asymptotic approximation of an integral involved in the calculation of the mass renormalization of the quantum scalar field and of the third symmetric elliptic integral are given as illustrations.     

Asymptotic Expansions of Generalized Stieltjes Transforms of Algebraically Decaying Functions

Asymptotic expansions of Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative integer powers of their variable have been exhaustively investigated by R. Wong. In this article, we extend this analysis to Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative rational powers of their variable. Distributional approach is used to derive asymptotic expansions of the Stieltjes and generalized Stieltjes transforms of this kind of functions for large values of the parameter(s) of the transformation. Error bounds are obtained at any order of the approximation for a large family of integrands. The asymptotic approximation of an integral involved in the calculation of the mass renormalization of the quantum scalar field and of the third symmetric elliptic integral are given as illustrations.     

Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters

We study a test statistic based on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U-statistic of order 4 with degeneracy of order 1. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular, size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.     

Optimizing the smoothed bootstrap

In this paper we develop the technique of a generalized rescaling in the smoothed bootstrap, extending Silverman and Young's idea of shrinking. Unlike most existing methods of smoothing, with a proper choice of the rescaling parameter the rescaled smoothed bootstrap method produces estimators that have the asymptotic minimum mean (integrated) squared error, asymptotically improving existing bootstrap methods, both smoothed and unsmoothed. In fact, the new method includes existing smoothed bootstrap methods as special cases. This unified approach is investigated in the problems of estimation of global and local functionals and kernel density estimation. The emphasis of this investigation is on theoretical improvements which in some cases offer practical potential.