UMVUE OF POLYNOMIALS OF (EX)~(-1) FOR SEVERAL NATURAL EXPONENTIAL FAMILIES ON THE POSITIVE LINE

1. IntroductionBecause of its applications ill biological science and econometrics as well as in experimental nuclear physics, some authors[1'2] have studied the unbiased estimation of the inverse ofpopulation mean! 1/m. Srivatava and Bhatnagar used the statisticXti '~ ~ k > 0, (1.1)X. k(4)'where k is a scalar constant abed s: is the unbiased sample variance, to estimate 1/m forany distribution with the third moment. They proved that ti is an asymptotically unbiasedestimator with bias of or…     

IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

Let x_1,…, x_n be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Z_n=(x_(1),…, x_(k), r(x)),where x_(i)(i=1,…, n) is the order statistic of x_i, i=1,…, n and k=k(x) is the num-ber of the observed data. Suppose that the distribution family of x_i, i=1,…, n is i.i.d.exponential with life expectation θ>0. For testing the hypothesis H_0: θ≤θ_0 againstH_1: θ>θ_0, we use the total time of experiment S_r=sub from i=1 to k x_(i) +(n-k)r (x) as the teststatistic. We reject H_0 as large value of S_r is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r_0 is the one which has the minimnm total experiment time.     

PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the thresh-old parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.     

ON CONSTRUCTING THE NATURAL EXPONENTIAL FAMILIES WITH POLYNOMIAL VARIANCE FUNCTIONS

In this paper,we discuss the regular exponential family(REF),a natural exponentialfamily with minimum dimension and with the mean function m=E_θX taken as a new parameter.Wepoint out the importance of the REF with polynomial variance function(PVF-REF).When m is asingle factor of PVF and the left end of its defined domain is zero,the corresponding REF is givenas the single-side lattice distribution family;other PVF-REFs can be obtained by a limit process.As an illustration,the results for all seven cases of polynomial variance functions of third degreeare given.     

EB RULES FOR SELECTING THE BEST EXPONENTIAL POPULATION

In this paper,we obtain empirical Bayes(EB)procedures for selecting the bestamong k different exponential populations(the form of the conditional probability densitye.g.each population is f_4(x_i/b_i)=b_i exp(-b_ix_i),x_i,b_i∈(0,∞),i=1,2,…,k).These rulesare based on the EB estimators of b_i.We show that,under the squared error loss,the Bayesrisk of the EB estimators converges to the related minimum Bayes risks with rates of conver-gence at Jeast of order O(n~(-q)).Further,for the selection problem,the rates of convergenceof the proposed selection rules are shown to be at least of order O(n~((-q)/2) where q can bearbitrarily close to 1/5 or 1 under suitable conditions.     

ASYMPTOTIC PROPERTIES OF MLE IN EXPONENTIAL FAMILY NONLINEAR MODELS

1.IntroductionSupposethattherandomvariablesyi5y2,'',y.areindependentandeachyihasdensity:withrespecttoaa-finitemeasurev,whereb,c,]areknownl'unctions;fiisaknownq-vectordefinedinX,Pistheunknownp-vectorparameterdefinedinB,oiisthenaturalparameter,andaisascaleparameter.Then(1)iscalledtheexponentialfamilynonlinear..dels[2]whicharenaturalextensionofgeneralizedlinearmodelsandnormalnonlinearmodels.Inthispaper,wegeneralizetheasymptoticresultof[1]and[3,4]toexponentialfamilynonlinearmodels.Section2gives…     

D-SThBILITY TESTING FOR THE INTERVAL MATRIX FAMILY

*ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionConsiderarealintervalmatrixfamilydefinedbyA={A=(qij),,..,Iqij5qij5q;,fori,j=1,2,'',n}(l.1)whichisasuperrectangleinlynxswithdimensionnxn.ForanyACA,leta(A)denotethesetoftheeigenvaluesofA.Definition1GivenanyopenandconnectedregionDinthecomplexplaneC,whichissymmetricabouttherealaxis.AissaidtobeD-stableifforeachAEA,a(A)CD.SincethepublicationofKharitonovTheorem[1],aconsiderableportionofresearchhasbeenaimeda…     

ESTIMATION AND INFERENCE FOR VARYING-COEFFICIENT REGRESSION MODELS WITH ERROR-PRONE COVARIATES

This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates. The authors focus on the situation where the covariates are unobserved, there are no repeated measurements and the covariance matrix of the measurement errors is unknown, but some auxiliary information is available. The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions, and show that the estimator achieves the optimal nonparametric convergence rate, is asymptotically normal, and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods. A simulation is carried out to study the finite sample performance of the proposed estimator, and a real date set is analyzed to illustrate the usefulness of the developed methodology.     

QUANTUM THEORY FOR THE BINOMIAL MODEL IN FINANCE THEORY

In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of R3, whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of N distinguishable particles.     

THE EXPONENTIAL BOUND OF THE SURVIVAL FUNCTION ESTIMAATOR FOR RANDOMLY TRUNCATED AND CENSORED DATA

ＴＨＥＥＸＰＯＮＥＮＴＩＡＬＢＯＵＮＤＯＦＴＨＥＳＵＲＶＩＶＡＬＦＵＮＣＴＩＯＮＥＳＴＩＭＡＡＴＯＲＦＯＲＲＡＮＤＯＭＬＹＴＲＵＮＣＡＴＥＤＡＮＤＣＥＮＳＯＲＥＤＤＡＴＡＺＨＵＹｕｊｉｅ（ＨｕｚｈｏｕＴｅａｃｈｅｒ＇ｓＣｏｌｌａｇｅ，Ｈｕｚｈｏｕ３１...     

THE TAIL ESTIMATION FOR THE DISTRIBUTION OF THE SUPREMA OF A P-BRIDGE

Let X_1,X_2,…be a sequence of independent random vectors which take values in IR~2 and X_i～P.By the projection pursuit (PP) method,we canconstruct PP type Kolmogrov-Smirnov statistics:K_n=(?) 1/n~(1/2)|sum from i=1 to n(I_|a~rX_(?)(?)t|-P(a~rX_1(?)t))|,where I_([·]) is the indicator function of the set [·] and P is a probability distribution.The limit distribution of K_n is the distribution for the suprema of a P-bridgewhose index is the set of all half spaces in IR~2.Let{W_p([0,(?)])∶(?)∈[0,1]~2} be atwo parameter Brownish bridge.The main result of this paper is(?)for all λ,provided P is the uniform distribution on [0,k_1]×[0,k_2],0相似文献   

ERROR ESTIMATION OF THE APPROXIMATION ALGORITHM FOR THE WINDY POSTMAN PROBLEM

If we restrict the postman to traversing each edge at most twice in the windypostman problem (WPP), we will get a new problem: 2WPP. An approximation algorithmhas been posed by M. Guan for the WPP. In the present paper, we improve the estimatederror given by M. Guan and show that we can estimate the error for the 2WPP by findinga minimum cost circulation. We also pose a new sufficient condition for the equivalencebetween WPP and 2WPP, which can be checked in polynomial time steps.     

ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS

1.IntroductionSomefrequentlyusedalgebraicalgorithmssharethesamepropertythattheytransformasetofpolynomialequationstoasinglepolynomialequationsuchthatthezerosetofthepolynomialsetandthehypersurfacedefinedbythesinglepolynomialareequivalentincertainsense.FOralgorithmswiththisproperty,wemaymention'thealgorithmtofindaprimitiveelementforafinitelygeneratedalgebraicextensionfield[1],thealgorithmtofindaplanecurvewhichisbirationaltoaspacealgebraiccur.e[2]!etc.Inthispaper,wepresentageneralalgorithmwhichcan…     

ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS

In this paper,an invariant determined by a function used to guarantee the convergence of all members with ι≤κ in the family of deformed Halley iterative methods for solving nonlinear equation in complex field is given.Results include some known ones as this special cases.We get not only the error estimates of the iterative sequences ｛zn,ι｝ but also those of f(zn,ι) for all ι≤κ.     

精选－优化辅助变量法对于闭环参数估计的收敛性

本文用连带微分方程（ＯＤＥ）方法分析了精选－优化辅助变量法对于闭环系统的参数估计的收敛特性，给出了收敛性的条件。这样就为用该辨识算法实现有效自适应控制系统设计提供了理论依据。     

三元行偶的优化理论及方法

引入行偶及其亏值的概念，证明了行偶亏值定理，在此基础上解决了把６个平行工序调整为３对顺序对的最优排序方法     

AN EMPIRICAL BAYES TWO-SIDED TEST PROBLEM FOR CONTINUOUS ONE-PARAMETER EXPONENTIAL FAMILIES

An empirical Bayes(EB)two-sided test problem about the continuousone-parameter exponential family has been discussed.We construct the EB test decisionrule and prove its asymptotical optimality.Further,we get its convergence ratesO(n~(-(λ(s-2))/(2s 1))under suitable conditions,where 0<λ<2,and s>2 is a given natural number.Finally,some examples about the result of the convergence rates are given.     

Box—Cox变换模型模拟矩估计方法研究

基于对Ｂｏｘ－Ｃｏｘ变换模型参数估计方法的研究，分析了极大似然方法之不足，提出了相应参数估计方法——基于残差的广义模拟矩估计方法，并研制了相应的算法．该方法同时解决了Ｂｏｘ－Ｃｏｘ变换模型出现序列相关与异方差时的参数估计问题，力求反映真实模型．算例则验证了方法的有效性     

FUZZY MODELS FOR ESTIMATION OF SURFACE GROUND SUBSIDENCE

In this paper,the mathematical theory of fuzzy probability is used for theproblems of rock mass mechanics due to excavation,especially mining.A mathematicalmodel is developed for the movement and deformation of rock mass on the basis of theassumption that the displacement and deformation of rock mass is a fuzzy event,and fromthis model theoretical formulas are derived for calculating the displacement of rock massdue to excavationThe theories of both the two-and three-dimensional problems are developed and appliedto the analysis of engineering problems in excavation.The agreement of the theoreticalresults with the field measurements shows that our model is satisfactory and the formulaeobtained are valid and thus can be effectively used for predicting the displacements anddeformations and the safety evaluation of the buildings on the ground surface.     

基于约束理论的一个管理决策NLP模型

在并行工程环境下，很广泛的一类管理决策过程可归结为一类线性约束ＮＬＰ模型，本文依据约束理论（ＴＯＣ）给出了确定“瓶颈”约束的定量方法，并提出了通过增加“瓶颈”约束的资源以有效地提高管理决策的整体综合效益的模型流程。