A LAW OF THE ITERATED LOGARITHM FOR RANDOM WINDOW-WIDTH KERNEL ESTIMATOR OF A NONPARAMETRIC REGRESSION FUNCTION

In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These results give sharp pointwise rates of strong consistency ofthese estimators.     

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA

1 IntroductionLet (X, T, Y) denote random variables where X is the variab1e of interest, called the lifetimevariab1e, with distribution function (d.f.) F; T is the random 1eft truncation time with arbitraryd.f G and Y is the random right censoring time with arbitrary d.f. H. It is assumed that Xis independent Of (T, Y), bnt T and Y may be dePendent and, Without 1oss of generality thatthey are nonnegative. In the random 1eft truncation and right censoring (LTRC) model oneobserves (Z, T…     

BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE

1.IntroductionConsiderthefixeddesignnonparametricregressionmodelK=g(xi) ei,i21,(1.l)whereg(x)isanunknownregressionfunctiondefinedontheinterval[0,if,{xi,iZ1}arefixeddesignpoilltsdrawnfromtheinterval[0,1],{ei,i21}arei.i.d.randomvariablesfromapopulationhavingunknownsymmetricdistributionF(x)withsymmetricpoint0andK(i21)istheobservationatxi(i21).Forestimatingtheunknownregressionfunctiong(x),takethefirstnobservationsYI,'',Ye.WithoutlossofgeneralityjletalSxZS''5xu.LetD.i(x)denotethei-thnearestn…     

THE BERRY-ESSEEN BOUND AND LIL PP CM STATISTIC TESTING UNIFORM DISTRIBUTION ON SPHERE ABOUT DIMENSION AND SAMPLE SIZE

1. IntroductionXI, Xz,'' I Xu are i.i.d. p dimension random vectors with distribution function F(x).Cuilzldefined PP Cramer-Von Mises test statistic as follows:where F:(x) ~ (Z:=, I[a'Xi 5 x])/n is the empirical distribution function of a'XI, a'X2,' ', a'X.. F"(x) ~ P(a'X, 5 x) is distribution function of a'XI, p(.) is uniform measuxeon SP--1. Under null hypothesis HO: XI has uniform distribution on SP--1, F"(x) 2 G(x) =if, g(u)du, where g(u) ~ {r(p/2)(1 -- u')(P--')/'}/{(r(1/2…     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

LIMIT LAWS OF LIFETIME FOR A CONSECUTIVE K-WITHIN-M-OUT-OF-N SYSTEM

ＬＩＭＩＴＬＡＷＳＯＦＬＩＦＥＴＩＭＥＦＯＲＡＣＯＮＳＥＣＵＴＩＶＥＫ－ＷＩＴＨＩＮ－Ｍ－ＯＵＴ－ＯＦ－ＮＳＹＳＴＥＭ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂｏｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ...     

ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

1.IntroductionWeconsidertheinitial-boundaryvalueproblem(IBVP)forscalarviscousconservationlaw(ut f(u).=uxx,xE(0, co)=R ,t>0,o,(n --9,ifI~9,f~M(IBVP){u(0't)=u~(t)-1~i---t:7),[u(x,0)=u000={=:0)f:LO .,wheref(u)>0foralluunderconsideration,andu--u (1.1),andu~(t)~u~EL'(R ),U'(t)EL'(R ).(1.2)Undercondition(1.l)or(l.l)',thecorrespondingRiemannproblem{;;ot:<:>;i,>=x{,:3'f:,:(13)yieldstherarefaCtionwavesolution(u~)x5f'(u~)t,r(X,t)=17j,)~1(…     

STRONG LAWS OF LIFETIME FOR A CONSECUTIVE K-OUT-OF-N: F SYSTEM

ＳＴＲＯＮＧＬＡＷＳＯＦＬＩＦＥＴＩＭＥＦＯＲＡＣＯＮＳＥＣＵＴＩＶＥＫ－ＯＵＴ－ＯＦ－Ｎ：ＦＳＹＳＴＥＭ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｇ，Ｂｅｉｊｉ...     

ASYMPTOTIC ANALYSIS OF THE OPTIMAL CONTROL OF AN ELASTODYNAMIC SYSTEM

Based on the idea of the reduction of optimal control systems in singularperturbations of Lions and a priori estimates in [4], we prove the convergence of theoptimal control, state and the cost function between a singular linear elastodynamic systemand a limit system. Our asymptotic analysis is applicable to the optimal control of flexiblerobotic manipulators.     

THE DISTRIBUTION OF LIMIT POINTS OF INCREMENTS OF LOCAL TIME OF THE WIENER PROCESS

ThisresearchissupportedbythePostdoctoralGrantofChina.1.IntroductionLetW(t)for05t相似文献   

上证股市收益的长期记忆:基于V/S 的经验分析

运用V/S分析考察我国股市收益的长期记忆效应,分别诊断上证A、B股市日收益总体样本的长期记忆效应,在运用ICSS方法探测方差漂移突变划分股票市场阶段性的基础上诊断股市收益不同阶段的长期记忆效应,并考察随机抽取的部分个股.研究表明:上证A、B股市收益总体样本都不存在显著的长期记忆,B股市场的长期记忆效应相对更显著;A、B股市场收益分别发生了两次和四次显著的方差漂移突变;A股收益在每一阶段都不存在显著的长期记忆,B股收益在某些阶段却存在显著的长期记忆.对随机抽取的10只个股的考察,发现只有1只股票的收益序列存在显著的长期记忆,B股收益的长期记忆效应相对比A股显著.     

ESTIMATION METHOD FOR SOLUTIONS TO GENERAL LINEAR SYSTEM OF VOLTERRA INTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRAL FUNCTIONALS

1. IntroductionThe study of Volterra-type integral inequalities had aroused much research illterest on thepart number of authors. In recent years, various VOlterra inequalities involving iterated illtegralfunctionals have also been investigated. We refer to 11--14] for related results for such inequalitiesin one independent variable. However, there is no result reported in the literature which isconcerned with arbitrary finite systems consisting of such integral inequalities. Obviously suchk…     

THE SYMMETRY GROUPS OF NONLINEARITY CRITERIA

It is already known that there are several nonlinearity criteria such as algebraic degree, nonlinearity,distance to linear structures, correlation immune, propagationcriterion, differential uniformity,which are used to check whether a cryptographic functionis weak or not. In this paper we will discuss these criteria from a valuation point of view,and consider the largest transformation group which leave a criterion invariant, which isnamed its symmetry group. It can serve as a way of comparing the stability of nonlinearitycriteria under the action of invertible transformations.     

ON THE COMPLEX OSCILLATION OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.     

关于争夺制天权的思考

当今世界,新技术革命的大潮汹涌澎湃,政局激烈动荡,战略格局正处在重新组合与调整时期。战略核武器的存在和持续发展与航天技术巨大成就和飞速进步交织在一起,使世界进入了“天核重叠”时代。地球上的缓和与对话,掩盖着太空的对抗与争夺。随着美国“战略防御倡议”计划的推进和实施,“星球大战”的设想和前景给未来太空的开发和利用罩上一层朦胧的阴影。未来的太空景象如何?随着航天技术的发展,开发太空将对人类社会的经济生活、政治生活和军事对抗态势产生何种影响?本文从宏观战略和科学技术角度,对有关问题做了分析、论述。     

THE LINEAR ARBORICITY OF COMPOSITION GRAPHS

The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G) 1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.     

重建目标特性的逆散射方法

本文综述由空间局部区域所测得的散射数据重建目标特性的逆散射方法,分别介绍分层介质特性剖面反演,波不可透入目标的形状重建,以及波可透入目标特性反演等问题。     

THE RATE OF UNIFORM CONVERGENCE OF THE SURVIVAL FUNCTION ESTIMATOR FOR TRUNCATED AND CENSORED DATA

1 Illtroduction and Main ResultsIn medical follow-up or engineering life testing studies one may not be able to observethe variable of inferest, referred to hereafter as the lifetime. Among the differellt forms inwhich incomplete data appears right censoring and left truncation are two common ones. Lefttruncation mad occur if the time origin of the lifetime precedes the time origin of the study.Only subjects that fail after the start of the study are being followed, otherwise they are lefttru…     

ON CONVERGENCE AND RATE OF CONVERGENCE OF ALGORITHMS IN THE MOVER－STAYER MODEL

ＯＮＣＯＮＶＥＲＧＥＮＣＥＡＮＤＲＡＴＥＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＡＬＧＯＲＩＴＨＭＳＩＮＴＨＥＭＯＶＥＲ－ＳＴＡＹＥＲＭＯＤＥＬＷＡＮＧＤｏｎｇｑｉａｎ；Ｌａｗｏｋｏ，Ｃ．Ｒ．Ｏ．（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＭａｓｓｅｙＵｎ...