Choice of optimal trimming proportion by the random weighting method

In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the distribution of some adaptive estimator is also obtained.Supported by the NNSF of China and the Doctoral Foundation of the Institutions Higher Learning of China     

ON THE CONSISTENCY OF CROSS-VALIDATIONIN NONLINEAR WAVELET REGRESSION ESTIMATION

1IntroductionConsidernonparametricregressiollwherextli=;E[O,1],En1,.',Ejl1larei.d.d.errorswitl11llea11o,a11dgisanunkl1ownfunctiontobeestimated-Nouparametricregressionestil11ationaimstoesti111atetl1euukllow11regressionfunctiong(x).Tl1enolllinearwaveletesti111atorshavebeenintroducedalldstudiedbyDonoho(1995).DonohoandJohnstoue(1994,1995).Do11oho,Johnstolle-KerkyachariallandPicard(1995)andDelyollandJuditsky(l996).Tl1eseauthorshavedenlo11stratedthevirtuesofllonlineaxwaveletmetl1odsf1o1llthev…     

二值回归模型中自变量误差的处理

In this paper the binary regression model, in which the response Y is binary, i.e. Y takes the value 0 or 1 only, is considered. The conditional probability P{Y=1|X=x} is assumed to be of the form G(a₀+a₁x), where x is the measurement of the factor, a= (a₀,a₁)′ is the vector of the unknown parameter being estimated and G(a) = (1+e^a)^-1. The measurement x is assu-med to be contaminated when the value of x is out of certain limit. M-estimation is employed to estimate the unknown a of the model. In this paper, the consistent M-estimation is proved to be asymptotically normal and the optimal M-equation is obtained. Finally, a computation method is introduced to solve the M-equation and to get the optimal solution.     

Random weighting method forT statistic

In this paper we deal with the measure model with independently distributed errors. For estimating the error distribution of the sample mean, random weighting method is utilized. It is proved that the accuracy of the approximation is of the order ofo (1 /n), which is the ideal rate.     

Gauss因果模型中因果效应识别方法的比较

一个Gauss因果模型中常常存在不只一种识别因果效应的方法, 不同的方法对应的估计可能不同. 该文对Pearl等人提出的前门准则, 后门准则,工具变量准则等识别方法的估计精度进行了分析比较, 并给出了相应的模拟结果, 为实践中选择更优的识别准则提供了依据.     

系统树中的近似Bayes方法

本文利用近似Ｂａｙｅｓ方法对一个具有树形结构的成败型系统的可靠性进行估计．本文证明了利用近似Ｂａｙｅｓ方法对系统的可靠性参数的估计，具点估计在Ｆｉｓｈｅｒ意义下是渐近有效的，其相应的置信下限也是Ｆｉｓｈｅｒ意义下渐近有效的．     

BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

1.IntroductionTheestimationofpopulationquaillesisofgrestillterestwhenone.isnotpreparedtoassumeaparametricformfortheunderlyingdistribution.Inaddition,quaillesoftenariseasthensturalthingtoestimatewhentheunderlyingdistributionisskewed.LetXIIXZ,')Xubei...     

VIRTUAL SYSTEM METHOD FOR SYSTEM TREE

ＶＩＲＴＵＡＬＳＹＳＴＥＭＭＥＴＨＯＤＦＯＲＳＹＳＴＥＭＴＲＥＥ￥ＺＨＥＮＧＺＨＯＮＧＧＵＯ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＢｅｉｊｉｎｇＵｎｉｖｅｒｓｉｔｙ）Ｂｅ１Ｊｉｎｇ１００８７１，Ｃｈｉｎａ．）（Ｐ...