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本文考虑纵向数据下半参数回归模型: $y_{ij}=x_{ij}'\beta+g(t_{ij})+e_ij},\;i=1,\cdots,m,\;j=1,\cdots,n_i$. 基于最小二乘法和一般的非参数权函数方法给出了模型中参数$\beta$和回归函数$g(\cdot)$的估计, 并在适当条件下证明了$\beta$估计量的渐近正态性和$g(\cdot)$估计量的最优收敛速度\bd 模拟结果表明我们的估计方法在有限样本情形有良好的效果 相似文献
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考虑方差分量模型$\ep Y=X\beta,\;\cov(Y)=\tsm_{i=1}^{m}\theta_iV_i$, 其中$n\times p$矩阵$X$和非负定矩阵$V_i\;(i=1,2,\cdots,m)$都是已知的, $\beta\in R^p,\;\theta_i\geq 0$或$\theta_i>0\;(i=1,2,\cdots,m)$均为参数\bd 在本文中, 我们在二次损失下, 当$\mu{(X)} \subset\mu{(V)}$时, 给出了关于可估函数$S\beta$的线性估计在线性估计类中可容许性的充要条件 相似文献
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本文研究了多元线性模型当未知参数受不完全椭球约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$时线性估计的可容许性问题.具体而言,我们研究了约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$中$N$和非中心点$\Theta_1$对线性估计的可容许性的影响.主要结果表明在两个不同的不完全椭球约束条件$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$与$\mbox{tr}(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2$ 下,当$\Theta_1$和$\Theta_2$满足一定的关系时,可容许的齐次线性估计类是相同的. 相似文献
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本文证明了自正则化Davis大数律和重对数律的精确渐近性, 即
{\heiti\bf 定理1}\hy 设$\ep X=0$, 且$\ep X^2I_{(|X|\leq x)}$在无穷远处是缓变函数, 则$\lim_{\varepsilon\searrow0}\varepsilon^2\tsm_{n\geq3}\frac{1}{n\log n}\pr\Big(\Big|\frac{S_n}{V_n}\Big|\geq\varepsilon\sqrt{\log\log n}\Big)=1.${\heiti\bf 定理2}\hy 设$\ep X=0$, 且$\ep X^2I_{(|X|\leq x)}$在无穷远处是缓变函数, 则对本文证明了目正则化Davis大数律和重对数律的精确渐近性,即定理1设EX=0,且EX~2I_(|x|≤x)在无穷远处是缓变函数,则■定理2设EX=0,且EX~2I_(|x|≤x)在无穷远处是缓变函数,则对0≤δ≤1,有■其中N为标准正态随机变量. 相似文献
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本文讨论区间数据情况下, 指数分布参数的估计\bd 引入了两种叠代方法, 证明了在一定的条件下, 叠代过程的收敛性. 相似文献
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令\{$X$, $X_n$, $n\ge 1$\}是期望为${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$和协方差阵为${\rm Cov}(X,X)=\sigma^2I_m$的独立同分布的随机向量列, 记$S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. 对任意$d>0$和$a_n=o((\log\log n)^{-d})$, 本文研究了${{\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$的一类加权无穷级数的重对数广义律的精确速率. 相似文献
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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. 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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Random weighting method for Cox’s proportional hazards model 总被引:1,自引:0,他引:1
Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals. 相似文献
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Xiaorong Yang Naveen Naidu Narisetty Xuming He 《Journal of computational and graphical statistics》2018,27(2):417-425
Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly censored data. In this article, we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data. Supplementary material for this article is available online. 相似文献
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Somnath Datta Glen A. Satten John M. Williamson 《Annals of the Institute of Statistical Mathematics》2000,52(1):160-172
Satten et al. (1998, J. Amer. Statist. Assoc., 93, 318–327) proposed an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations which are the score equations for the full data proportional hazards model, averaged over all rankings of imputed failure times consistent with the observed censoring intervals. In this paper, we extend this approach to incorporate data that are left-truncated and right censored (dynamic cohort data). Consistency and asymptotic normality of the estimators obtained in this way are established. 相似文献
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《Journal of Computational and Applied Mathematics》2002,149(2):373-380
Censoring models are frequently used in reliability analysis to reduce experimental time. The three types of censoring models are type-I, type-II and random censoring. In this study, we focus on the right random censoring model. In this model, if the failure time exceeds its associated censoring time, then the failure time becomes a censored observation. In this case, many authors (see: Lee, Statistical Methods for Survival Data Analysis, 2nd Edition, Wiley, New York, 1992; Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 1982; Miller, Survival Analysis, Wiley, New York, 1981, among others) considered using the observed censoring time to impute the censored observation which, however, underestimates the true failure time. Herein, two methods to impute the censored observations are proposed in a right random censoring model for a 2-parameter Weibull distribution. By a Monte Carlo simulation, the quantile estimates are calculated to assess the performance of the proposed imputation methods with respect to their relative mean square error. Simulation results indicate that the two imputation methods proposed herein are superior to the method proposed by the above authors if the shape parameter of Weibull distribution exceeds 1, except for the lower quantiles. 相似文献
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The validity of a diagnostic marker can be summarised by using statistical measures either for the goodness of the fit like the deviance, measures of the explained variation like R2 or the misclassification rate. Other intuitive measures are sensitivity and specificity in the case of binary response. In the absence of censored data the calculation of these measures is widely used. In the presence of censoring the estimation of time-dependent sensitivity and specificity is not well known. In this article we propose a new method for calculating ROC curves with censored data using the observed number of events and calculating the additional number of expected events for censored observations. The new method is illustrated with data for predicting mortality in patients surviving a myocardial infarction. 相似文献
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Zheng Zukang 《数学年刊B辑(英文版)》1988,9(2):167-175
Let X_1,…,X_n be a sequence of independent identically distributed random variableswith distribution function F and density function f.The X_are censored on the right byY_i,where the Y_i are i.i.d.r.v.s with distribution function G and also independent of theX_i.One only observesLet S=1-F be survival function and S be the Kaplan-Meier estimator,i.e.,where Z_are the order statistics of Z_i and δ_((i))are the corresponping censoring indicatorfunctions.Define the density estimator of X_i by where =1-and h_n(>0)↓0. 相似文献
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Jian-Jian Ren 《Annals of the Institute of Statistical Mathematics》2001,53(3):498-516
We propose a procedure to construct the empirical likelihood ratio confidence interval for the mean using a resampling method. This approach leads to the definition of a likelihood function for censored data, called weighted empirical likelihood function. With the second order expansion of the log likelihood ratio, a weighted empirical likelihood ratio confidence interval for the mean is proposed and shown by simulation studies to have comparable coverage accuracy to alternative methods, including the nonparametric bootstrap-t. The procedures proposed here apply in a unified way to different types of censored data, such as right censored data, doubly censored data and interval censored data, and computationally more efficient than the bootstrap-t method. An example of a set of doubly censored breast cancer data is presented with the application of our methods. 相似文献