比例优势模型在多结局区间截断数据上的应用

探索比例优势模型在临床医学中常见的多结局区间截断数据中的应用.用条件的逻辑回归方法避免讨厌参数的估计,用牛顿-拉普森算法估计回归系数,用＂夹心方差＂估计量作为参数方差的估计.通过随机模型检验模型应用的有效性.     

k-正态分布及其应用（英文）

近本文研究了截断随机变量和k-正态分布.利用对数凹函数理论,获得了涉及截断随机变量和截断随机变量的函数的方差的不等式链,推广了涉及正态分布和分层教学模型的一些经典结论.同时在附录部分给出了仿真结果.     

关于区间数据的分布函数估计问题

随机变量的区间观察值是指在随机试验中，我们只知道随机变量X是否落入某个可以观察的区间(TL，TR](该区间可以是来自某个已知或未知的二维分布)，但不知道随机变量X的具体观察值．这类问题不同于以往讨论过的左截断，右截断或双侧截断问题．本文将所见到的一些有关分布函数方面的研究成果作了一个简要介绍，同时也给出了作者的最新研究结果．     

k-正态分布及其应用

近本文研究了截断随机变量和k-正态分布.利用对数凹函数理论,获得了涉及截断随机变量和截断随机变量的函数的方差的不等式链,推广了涉及正态分布和分层教学模型的一些经典结论.同时在附录部分给出了仿真结果.     

变量为区间截断数据时回归模型的参数估计(英文)

在假设自变量X的分布为离散未知分布且样本为区间截断数据而因变量Y是可观察的情况下,利用EM方法得到了回归参数的极大似然估计,在一定的条件下估计量的分布为渐近正态的.     

截断数据模型中的两阶段抽样序贯密度估计

令X_1,X_2,…是iid随机变量序列,满足分布F密度函数f.X_i被随机变量Y_i右截断,而Y_i是iid随机变量,且与X_t独立。我们仅能观察到样本 Z_i=min(X_i,Y_i),δ_i=I(X_i≤Y_i)估计量f_n和_n是基于KM估计量的f的核型估计,在本文中,我们基于f_n和_n分别构造f的两阶段抽样的序贯固定长度2d,渐近置信系数1-α。(0<α<1)的置信区间。并讨论了停时的渐近性质。     

有限个均匀分布随机变量之和的分布

<正> 均匀分布是一种最简单而又较常见的分布,有着较广的应用.本文讨论在任意一个区间中有限个相互独立均匀分布的随机变量之和的分布问题. 首先讨论均匀分布的区间长度相等的情况. 设η_1,η_2,…η_n是在区间(0,1)中n个相互独立的均匀分布的随机变量,令η=η_1+     

随机截断模型下的中心极限定理

在流行病学,生物统计学和天文学中常遇到随机截断数据.在随机截断下,人们关心的随机变量X被另一个随机变量y干扰.只有当X≥y时,才能观测到X和Y.在这个模型下,人们需要用截断数据估计X的分布函数F.本文证明,F的非参数最大似然估计Fn在下述意义下服从中心极限定理.对任何可测函数g(x),√n∫f9(x)[dFn(x)-dF(x)]依分布收敛到均值为零方差为σ2的正态分布.从这个结果可以得出F的各种矩,特征函数等估计的渐近正态性.作为推论,还可以得到Fn在整个直线上的依分布收敛.我们的结果不要求X和Y的分布函数连续,得到的方差公式是简明的.     

随机截断模型下的中心极限定理

在流行病学,生物统计学和天文学中常遇到随机截断数据.在随机截断下,人们关心的随机变量X被另一个随机变量Y干扰.只有当X≥Y时,才能观测到X和Y.在这个模型下,人们需要用截断数据估计X的分布函数F.本文证明,F的非参数最大似然估计Fn在下述意义下服从中心极限定理.对任何可测函数g（x）,n~（1/2）∫g（x）[dFn（x）-dF（x）]依分布收敛到均值为零方差为σ2的正态分布.从这个结果可以得出F的各种矩,特征函数等估计的渐近正态性.作为推论,还可以得到Fn在整个直线上的依分布收敛.我们的结果不要求X和Y的分布函数连续,得到的方差公式是简明的.     

数据非随机缺失时单变量的分布函数估计

本文研究数据非随机缺失下的分布函数估计问题.在确定缺失数据是否属于某些指定区间的前提下,对一维随机变量y的分布函数F(y)作出了估计.此时,假定数据缺失机制形式已知,但包含某未知多维参数θ.本文证明了未知参数θ的估计量(θ)的相合性和渐近正态性,也证明了分布函数F(y)的估计量F(y)的相合性和渐近正态性.     

协变量区间删失时线性模型的参数估计

本文研究了当协变量为区间数据时的线性模型，通过构造区间数据变量的条件均值，得到了回归参数的估计，当协变量的分布已知时，证明了估计的无偏性与强相合性．时协变量的分布未知的情形也作了讨论．文中还作了若干模拟计算，从模拟的结果不难发现，利用本文提出的方法所获得的估计简便且具有较高的精度．     

Strong uniform consistency of kernel density estimators under a censored dependent model

Problems with censored data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this paper, the estimation of the density function by the kernel method is considered, when censored data show some kind of dependence. We apply the strong Gaussian approximation technique for studying the strong uniform consistency for kernel estimators of the density function under a censored dependent model.     

Asymptotic approximation of kernel-type estimators with its application

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.     

Asymptotic distributions of two “synthetic data” estimators for censored single-index models

The censored single-index model provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored and the link function is unknown. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure time models for survival analysis. This paper proposes two methods for estimation of single-index models with randomly censored samples. We first transform the censored data into synthetic data or pseudo-responses unbiasedly, then obtain estimates of the index coefficients by the rOPG or rMAVE procedures of Xia (2006) [1]. Finally, we estimate the unknown nonparametric link function using techniques for univariate censored nonparametric regression. The estimators for the index coefficients are shown to be root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodologies.     

The Estimation of Accelerated Failure Time Model with Right-Censored Data

The accelerated failure time model provides a natural formulation of the effects of covariates on the failure time variable. The presence of censoring poses major challenges in the semi-parametric analysis. The existing semi-parametric estimators are computationally intractable. In this article we propose an unbiased transformation for the potential censored response variable, thus least square estimators of regression parameters can be gotten easily. The resulting estimators are consistent and asymptotically normal. Based on these, we can get a strongly consistent K-M estimator for the distribution of random error. Extensive simulation studies show that the asymptotic approximations are accurate in practical situations.     

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.     

随机截尾下污染数据部分线性模型的强相合估计

考虑一类新的污染数据部分线性模型,当受污染后的因变量被随机右截断时,就截断分布已知的情形,利用所获得截断观测数据构造了模型中的参数分量,非参数分量及污染系数的估计量,并在适当的条件下,证明了这些估计量的强相合性.     

Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.     

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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.     

Tree-based multivariate regression and density estimation with right-censored data

We propose a unified strategy for estimator construction, selection, and performance assessment in the presence of censoring. This approach is entirely driven by the choice of a loss function for the full (uncensored) data structure and can be stated in terms of the following three main steps. (1) First, define the parameter of interest as the minimizer of the expected loss, or risk, for a full data loss function chosen to represent the desired measure of performance. Map the full data loss function into an observed (censored) data loss function having the same expected value and leading to an efficient estimator of this risk. (2) Next, construct candidate estimators based on the loss function for the observed data. (3) Then, apply cross-validation to estimate risk based on the observed data loss function and to select an optimal estimator among the candidates. A number of common estimation procedures follow this approach in the full data situation, but depart from it when faced with the obstacle of evaluating the loss function for censored observations. Here, we argue that one can, and should, also adhere to this estimation road map in censored data situations.Tree-based methods, where the candidate estimators in Step 2 are generated by recursive binary partitioning of a suitably defined covariate space, provide a striking example of the chasm between estimation procedures for full data and censored data (e.g., regression trees as in CART for uncensored data and adaptations to censored data). Common approaches for regression trees bypass the risk estimation problem for censored outcomes by altering the node splitting and tree pruning criteria in manners that are specific to right-censored data. This article describes an application of our unified methodology to tree-based estimation with censored data. The approach encompasses univariate outcome prediction, multivariate outcome prediction, and density estimation, simply by defining a suitable loss function for each of these problems. The proposed method for tree-based estimation with censoring is evaluated using a simulation study and the analysis of CGH copy number and survival data from breast cancer patients.