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本文针对双边删失数据讨论了生存函数的非参数Bayes估计问题,运用Fred-holm积分的一些经典结果,文中证明了该估计弱收敛的一个Gaussian过程。 相似文献
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随机删失数据下几种风险率函数估计的渐近性质 总被引:1,自引:0,他引:1
文中对于删失数据下几种不同的风险率函数估计进行了研究。使用与以往不同的方法,在较弱的条件下,改进并扩充了现有文献的结果,获得了这几种风险率函数估计的渐近正态性,一致强弱相合收敛速度以及重对数律且进行了数值模拟。 相似文献
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设(X,Y)是一随机向量且变量Y的均值存在.假定Y被另一分布G的随机变量t删失,仅能观察到不完全数据(xi,Yi^ti,δi),i=1,2,…n,其中Yi^ti=min(Yi,Ti),δi=I(Yi≤ti)。为了给出回归函数m(x)=E(Y|X)的估计。文中使用了Stute提出的最近邻型回归估计,并给出了该估计的强相合性结果. 相似文献
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本文在假设被删失变量与删失变量之间不独立的情形下,给出了被删失变量的密度函数的核估计形式,得到了密度函数估计的强—致收敛速度. 相似文献
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Tadashi Nakamura 《Annals of the Institute of Statistical Mathematics》1984,36(1):375-393
Summary A new type of random sample, called a generalized censored data sample, is defined. An approach to finding criteria for the
existence of a maximum likelihood estiamte from a finite generalized censored data sample is presented. This approach, named
the probability contents boundary analysis, gives systematically a number of practical criteria, each of which is effective
for various kinds of typical distribution families in statistical analysis. 相似文献
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A class of estimators of the mean survival time from interval censored data with application to linear regression 总被引:3,自引:0,他引:3
Zu-kang Zheng 《高校应用数学学报(英文版)》2008,23(4):377-390
A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency (with the rate of O(n^-1/1 (log log n)^1/2)) and asymptotic normality. The application to linear regression is considered and the simulation reports are given. 相似文献
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FANG Yixin JIN Man & ZHAO Lincheng Department of Statistics Finance University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(2):155-168
A regression model with a nonnegativity constraint on the dependent variable, known as censored median regression model, is considered. Under some mild conditions, the LAD estimate of the regression coefficient is shown to be strongly consistent. Furthermore, its convergence rate and Bahadur strong representation are also obtained. 相似文献
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Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed. 相似文献
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For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right_censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, Cp and FPE criteria in the process of selecting the parameters. 相似文献
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区间数据情形下线性模型的经验似然推断 总被引:2,自引:0,他引:2
He Qixiang Zheng Ming 《高校应用数学学报(英文版)》2005,20(3):338-346
§1Introduction Instatisticalapplications,weoftenencounterintervalcensoreddatawhenafailure timeYcannotbeobserved,butcanonlybedeterminedtolieinanintervalobtainedfroma sequenceofexaminationtimes.Forinstance,themaximumdosagewhichpatientscan endureisconcerned.LetYibethemaximumdosagewhichtheithpatientcanendure,Ui,j(j=1,2,...,k)bethedosagewhichthepatienthasbeentested.ItisobviousthatYiis unobservable.SupposetheithpatientisnormalwhenthedosageisUi,j,andhe(orshe)is abnormalwhenthedosageisUi,j+1.Then… 相似文献
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A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data 总被引:1,自引:0,他引:1
In this paper we consider the TJW product-limit estimatorFn(x) of an unknown distribution functionFwhen the data are subject to random left truncation and right censorship. An almost sure representation of PL-estimatorFn(x) is derived with an improved error bound under some weaker assumptions. We obtain the strong approximation ofFn(x)−F(x) by Gaussian processes and the functional law of the iterated logarithm is proved for maximal derivation of the product-limit estimator toF. A sharp rate of convergence theorem concerning the smoothed TJW product-limit estimator is obtained. Asymptotic properties of kernel estimators of density function based on TJW product-limit estimator is given. 相似文献
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Owen首次在完全样本下提出了经验似然的方法,WangQihua将该方法应用到带有截断情况的生存函数的函数估计问题.本文给出了更为一般的调整似然比统计量,证明了在适当的情况下该统计量仍渐近服从χ^2分布,同时模拟的结果也表明该统计量具有良好的性质。 相似文献
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ZHOU Xiuqing & WANG Jinde School of Mathematics Computer Science Nanjing Normal University Nanjing China. Department of Mathematics Nanjing University Nanjing China 《中国科学A辑(英文版)》2005,48(7):880-897
The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation. 相似文献
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Pao-sheng Shen 《Annals of the Institute of Statistical Mathematics》2011,63(6):1207-1219
Patilea and Rolin (Ann Stat 34(2):925–938, 2006) proposed a product-limit estimator of the survival function for twice censored data. In this article,
based on a modified self-consistent (MSC) approach, we propose an alternative estimator, the MSC estimator. The asymptotic
properties of the MSC estimator are derived. A simulation study is conducted to compare the performance between the two estimators.
Simulation results indicate that the MSC estimator outperforms the product-limit estimator and its advantage over the product-limit
estimator can be very significant when right censoring is heavy. 相似文献