Weibull分布定时截尾试验数据情形下的数据填充算法

利用处理非随机删失数据的矩不变准则及相应算法,本文针对Weibuu分布相同定时截尾型试验数据,通过控制算法中填充数据的分位概率,证明了通过迭代算法所得到的参数估计的相合性.进一步,通过对参数空间进行压缩,使得改进后的收敛算法所得到的参数估计同时具有相合性及不变性.作为本文算法的一个应用,我们还研究了利用填充后的虚拟完全样本构造可靠度的区间估计.最后,通过模拟计算验证了该算法具有较好的计算稳定性和可操作性.     

基于删失数据的ARMA模型参数估计与实证分析

利用生存分析中的K-M估计得到了删失数据下ARMA模型的参数估计,通过与完全数据下的参数估计进行对比,充分说明了该估计的效果.利用删失数据下ARMA模型的EM算法,对2013年5月2日到2014年5月8日的247个美元兑人民币的基准汇率数据进行建模分析和预测,并与实际数据进行对照,误差较小,说明估计和EM预测方法的可行性.     

超高维Ⅱ型区间删失数据的非参数变量筛选法北大核心CSCD

在定期随访的医学研究或临床实验中,人们经常会收集到高维区间删失数据,如何对这类数据进行降维是一个非常有意义的问题.本文基于Kolmogorov-Smirnov检验统计量,利用分割和融合的技巧,把独立特征筛选方法推广到区间删失数据中,提出了一种可以处理超高维Ⅱ型区间删失数据且不依赖于任何模型假设的变量筛选方法.此方法的适用范围很广,可以有效地处理各种生存模型下的超高维Ⅱ型区间删失数据,而且可以处理离散型,连续型等多种类型的协变量.在估计生存函数时,本文采用EM-ICM算法,极大地提高了计算效率.大量的数值模拟实验验证了此方法在有限样本下的有效性.     

Ⅰ型逐阶删失数据下基于EM算法的Weibull参数估计

研究了Ⅰ型逐阶删失数据下基于EM算法的Weibull参数估计,模拟产生不同Weibull参数组合和删失计划下的Ⅰ型逐阶删失数据,应用基于,EM算法的极大似然估计方法得到参数的估计值,并与数值方法得到的极大似然估计值进行对比,说明EM算法的估计效果.对73名肾脏移植患者生存数据进行实例分析,验证了基于EM算法的参数估计方法的可行性.     

纵向删失数据下线性模型的相合估计

医药临床试验,生存分析,可靠性统计等研究领域,由于考虑到时间和费用问题,研究往往有一定期限.因为研究到期的被迫结束或者某些病人中途退出试验,最后得到的试验结果往往是删失数据.对于删失数据,采用无偏转换的方法处理,方法的最大优点是得到的估计量为显式解.首先讨论了在纵向右删失数据下线性回归模型回归系数估计的均方相合性,并且把结论推广到了污染线性模型,得到了污染系数、回归系数的强相合估计.     

删失数据下医药费用的经验似然估计

生存时间数据删失问题是医药费用统计推断的一大难点,本文针对可以获得费用历史信息的情形,提出了在删失数据下医药费用的经验似然估计方法,给出在一定置信水平下感兴趣参数的置信区间.通过模拟,比较了在不同样本量下本文提出的方法与已有方法的表现,结果是我们的方法得到的置信区间更短,估计效果更好.同时,我们也针对一项心脏病实验的实际数据进行了相关分析和比较,得到满意的结果.     

部分线性模型参数极大似然估计的收敛速度

针对部分线性模型, 在其随机误差的分布函数属于刻度族, 刻度参数未知, 并且响应变量的观测值为区间删失数据的情形下, 讨论了其Sieve极大似然估计的强相合性和弱收敛速度.     

右删失时间序列AR模型参数估计

通过Kaplan-Meier估计和Nelson-Aalen估计得到了平稳时间序列被另一平稳序列右删失下.AR模型的参数估计.首先,通过与完全数据下的参数估计进行对比,说明了两种估计方法的效果.然后,根据计算机模拟的样本量以及删失率的不同,对比了两种估计的优劣,并且模拟结果表明两种估计是有效的.     

随机删失下半参数估计的强相合性

主要讨论了随机删失下的部分线性模型,利用基于分布函数的核估计和最小二乘法,给出了删失情况下参数和非参数部分的估计,并证明了它们的强相合性.     

左截断右删失数据分位差估计及其渐近性质

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计.利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性.同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.     

基于删失数据的指数威布尔分布最大似然估计的新算法

本文讨论了指数威布尔分布当观测数据是删失数据情形时参数的最大似然估计问题.因为删失数据是一种不完全数据,我们利用EM算法来计算参数的近似最大似然估计.由于EM算法计算的复杂性,计算效率也不理想.为了克服牛顿-拉普森算法和EM算法的局限性,我们提出了一种新的方法.这种方法联合了指数威布尔分布到指数分布的变换和等效寿命数据的技巧,比牛顿-拉普森算法和EM算法更具有操作性.数据模拟讨论了这一方法的可行性.为了演示本文的方法,我们还提供了一个真实寿命数据分析的例子.     

Weibull分布定时截尾试验数据情形下可靠度的置信限

本文针对Weibull分布定时截尾型试验数据提出了一种计算可靠度置信限的方法。通过采用数据填充的方式将不完全数据虚拟成完全数据,利用完全数据情形下可靠度置信限的计算方法得到删失数据情形下可靠度的置信限。模拟研究表明本文提出的算法具有较好的计算稳定性和可操作性。     

Nonparametric estimation of interval-censored failure time data in the presence of informative censoring

Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures (Kalbfleisch and Prentice, 2002). In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism (Sun, 2006; Turnbull, 1976). In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.     

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The hybrid censoring scheme is a mixture of type-I and type-II censoring schemes. It is a popular censoring scheme in the literature of life data analysis. Mixed exponential distribution (MED) models is a class of favorable models in reliability statistics. Nevertheless, there is no much discussion to focus on parameters estimation for MED models with hybrid censored samples. We will address this problem in this paper. The EM (Expectation-Maximization) algorithm is employed to derive the closed form of the maximum likelihood estimators (MLEs). Finally, Monte Carlo simulations and a real-world data analysis are conducted to illustrate the proposed method.     

Regression analysis of right-censored failure time data with missing censoring indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.     

Statistical Inference for the Rayleigh distribution under progressively Type-II censoring with binomial removal

This paper takes into account the estimation for the unknown parameter of the Rayleigh distribution under Type II progressive censoring with binomial removals, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. The expected termination point to complete the censoring test is computed and analyzed under binomial censoring scheme. Numerical examples are given to illustrate the approach by means of Monte Carlo simulation. A real life data set is used for illustrative purposes in conclusion.     

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In collecting clinical data, data would be censored due to competing risks or patient withdrawal. The statistical inference for censoring data is always based on the assumption that the failure time and censoring time is independent. But in practice the failure time and censoring time are often dependent. Dependent censoring make the job to deal with censoring data more complicated. In this paper, we assume that the joint distribution of the failure time variable and censoring time variable is a function of their marginal distributions. This function is called a copula. Under prespecified copulas, the maximum likelihood estimators for cox proportional hazards models are worked out. Statistical analysis results are carried by simulations. When dependent censoring happens, the proposed method will do better than the traditional method used in independent situations. Simulation results show that the proposed method can get efficient estimations.     

Adjusted Log-rank Test with Double Inverse Weighting under Dependent Censoring

It is a common issue to compare treatment-specific survival and the weighted log-rank test is the most popular method for group comparison. However, in observational studies, treatments and censoring times are usually not independent, which invalidates the weighted log-rank tests. In this paper, we propose adjusted weighted log-rank tests in the presence of non-random treatment assignment and dependent censoring. A double-inverse weighted technique is developed to adjust the weighted log-rank tests. Specifically, inverse probabilities of treatment and censoring weighting are involved to balance the baseline treatment assignment and to overcome dependent censoring, respectively. We derive the asymptotic distribution of the proposed adjusted tests under the null hypothesis, and propose a method to obtain the critical values. Simulation studies show that the adjusted log-rank tests have correct sizes whereas the traditional weighted log-rank tests may fail in the presence of non-random treatment assignment and dependent censoring. An application to oropharyngeal carcinoma data from the Radiation Therapy Oncology Group is provided for illustration.     

Life expectancy under random censorship

This paper deals with estimation of life expectancy used in survival analysis and competing risk study under the condition that the data are randomly censored by K independent censoring variables. The estimator constructed is based on a theorem due to Berman [2], and it involves an empirical distribution function which is related to the Kaplan-Meier estimate used in biometry. It is shown that the estimator, considered as a function of age, converges weakly to a Gaussian process. It is found that for the estimator to have finite limiting variance requires the assumption that the censoring variables be stochastically larger than the “survival” random variable under investigation.