随机截断模型下生存函数的一个估计

本文讨论截断数据生存函数的估计问题。由于在寿命试验中截断分布Ｇ（ｙ）往往是人们５自己设计的，从类似Ｂｕｃｋｌｅｙ和Ｊａｍｅｓ处理期望的思想出发，文中给出了一个新的估计，并计算了它的期望和方差。     

Asymptotic normality of wavelet density estimator under censored dependent observations

In this paper, we discuss the asymptotic normality of the wavelet estimator of the density function based on censored data, when the survival and the censoring times form a stationary ??-mixing sequence. To simulate the distribution of estimator such that it is easy to perform statistical inference for the density function, a random weighted estimator of the density function is also constructed and investigated. Finite sample behavior of the estimator is investigated via simulations too.     

A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples

In this paper, we discuss the estimation of a density function based on censored data by the kernel smoothing method when the survival and the censoring times form a stationary α-mixing sequence. A Berry-Esseen type bound is derived for the kernel density estimator at a fixed point x. For practical purposes, a randomly weighted estimator of the density function is also constructed and investigated.     

Censored multiple regression by the method of average derivatives

This paper proposes a technique [termed censored average derivative estimation (CADE)] for studying estimation of the unknown regression function in nonparametric censored regression models with randomly censored samples. The CADE procedure involves three stages: firstly-transform the censored data into synthetic data or pseudo-responses using the inverse probability censoring weighted (IPCW) technique, secondly estimate the average derivatives of the regression function, and finally approximate the unknown regression function by an estimator of univariate regression using techniques for one-dimensional nonparametric censored regression. The CADE provides an easily implemented methodology for modelling the association between the response and a set of predictor variables when data are randomly censored. It also provides a technique for “dimension reduction” in nonparametric censored regression models. The average derivative estimator is shown to be root-n consistent and asymptotically normal. The estimator of the unknown regression function is a local linear kernel regression estimator and is shown to converge at the optimal one-dimensional nonparametric rate. Monte Carlo experiments show that the proposed estimators work quite well.     

On estimation of survival function under random censoring model

We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation. A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain advantages over the common Kaplan-Meier estmator.     

Wavelet estimation of conditional density with truncated, censored and dependent data

In this paper we define a new nonlinear wavelet-based estimator of conditional density function for a random left truncation and right censoring model. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimators, the MISE expression of the wavelet-based estimators is not affected by the presence of discontinuities in the curves. Also, asymptotic normality of the estimator is established.     

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.     

The multiple imputations based Kaplan–Meier estimator

We derive the asymptotic distribution of the multiple imputations-based Kaplan–Meier estimator from right censored data with missing censoring indicators. We perform theoretical and numerical comparison studies with a competing semiparametric survival function estimator. We also carry out numerical studies to assess the performance of the proposed estimator when there is model misspecification.     

Optimal global rate of convergence in nonparametric regression with left-truncated and right-censored data

In this paper we consider nonparametric regression with left-truncated and right-censored data. An estimator of the regression function is developed when censoring and truncation are independent of covariates and the response. The estimation is based on the product limit estimator of the response variable. Under certain conditions, the L₂ rate of convergence of the estimated regression function is obtained when tensor products of B-splines are used.     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.     

Regression analysis of interval censored and doubly truncated data with linear transformation models

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. For double-truncated data, the lifetime T is observable only when U ≤ T ≤ V, where U and V are the left-truncated and right-truncated time, respectively. In some situation, the lifetime T also suffers interval censoring. This paper considers the estimation of regression parameters under linear transformation models, in the presence of interval-censored and doubly truncated (ICDT) data. It is demonstrated that the approach of Zhang et al. (Can J Stat 33:61–70, 2005) can be extended to analyze ICDT data. The asymptotic properties of the proposed estimator are discussed. A simulation study is conducted to investigate the performance of the proposed estimator.     

Estimation and confidence bands of a conditional survival function with censoring indicators missing at random

The nonparametric estimator of the conditional survival function proposed by Beran is a useful tool to evaluate the effects of covariates in the presence of random right censoring. However, censoring indicators of right censored data may be missing for different reasons in many applications. We propose some estimators of the conditional cumulative hazard and survival functions which allow to handle this situation. We also construct the likelihood ratio confidence bands for them and obtain their asymptotic properties. Simulation studies are used to evaluate the performances of the estimators and their confidence bands.     

Nonparametric estimators of the survival function with twice censored data

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.     

Survival function estimation when lifetime and censoring time are dependent

In this paper we consider a model for dependent censoring and derive a consistent asymptotically normal estimator for the underlying survival distribution from a sample of censored data. The methodology is illustrated with an application to the analysis of cancer data. Some simulations to evaluate the performance of our estimator are also presented. The results indicate that our estimator performs reasonably well in comparison to the other dependent censoring survival curve estimators.     

Multiple imputations and the missing censoring indicator model

Semiparametric random censorship (SRC) models (Dikta, 1998) provide an attractive framework for estimating survival functions when censoring indicators are fully or partially available. When there are missing censoring indicators (MCIs), the SRC approach employs a model-based estimate of the conditional expectation of the censoring indicator given the observed time, where the model parameters are estimated using only the complete cases. The multiple imputations approach, on the other hand, utilizes this model-based estimate to impute the missing censoring indicators and form several completed data sets. The Kaplan-Meier and SRC estimators based on the several completed data sets are averaged to arrive at the multiple imputations Kaplan-Meier (MIKM) and the multiple imputations SRC (MISRC) estimators. While the MIKM estimator is asymptotically as efficient as or less efficient than the standard SRC-based estimator that involves no imputations, here we investigate the performance of the MISRC estimator and prove that it attains the benchmark variance set by the SRC-based estimator. We also present numerical results comparing the performances of the estimators under several misspecified models for the above mentioned conditional expectation.     

Smooth estimation of survival and density functions for a stationary associated process using Poisson weights

Let {X_n,n≥1} be a sequence of stationary non-negative associated random variables with common marginal density f(x). Here we use the empirical survival function as studied in Bagai and Prakasa Rao (1991) and apply the smoothing technique proposed by Gawronski (1980) (see also Chaubey and Sen, 1996) in proposing a smooth estimator of the density function f and that of the corresponding survival function. Some asymptotic properties of the resulting estimators, similar to those obtained in Chaubey and Sen (1996) for the i.i.d. case, are derived. A simulation study has been carried out to compare the new estimator to the kernel estimator of a density function given in Bagai and Prakasa Rao (1996) and the estimator in Buch-Larsen et al. (2005).     

Doubly robust semiparametric estimation for the missing censoring indicator model

We present a semiparametric analysis of an augmented inverse probability of non-missingness weighted (AIPW) estimator of a survival function for the missing censoring indicator model. Although the estimator is asymptotically less efficient than a Dikta semiparametric estimator, its advantage is the insulation that it offers against inconsistency due to misspecification. We present theoretical and numerical comparisons of the asymptotic variances when there is no misspecification. In addition, we derive the asymptotic variance of the AIPW estimator when there is partial misspecification. We also present a numerical robustness study that confirms the superiority of the AIPW estimator when there is misspecification.     

Location estimation in nonparametric regression with censored data

Consider the heteroscedastic model Y=m(X)+σ(X)?, where ? and X are independent, Y is subject to right censoring, m(·) is an unknown but smooth location function (like e.g. conditional mean, median, trimmed mean…) and σ(·) an unknown but smooth scale function. In this paper we consider the estimation of m(·) under this model. The estimator we propose is a Nadaraya-Watson type estimator, for which the censored observations are replaced by ‘synthetic’ data points estimated under the above model. The estimator offers an alternative for the completely nonparametric estimator of m(·), which cannot be estimated consistently in a completely nonparametric way, whenever high quantiles of the conditional distribution of Y given X=x are involved.We obtain the asymptotic properties of the proposed estimator of m(x) and study its finite sample behaviour in a simulation study. The method is also applied to a study of quasars in astronomy.     

删失数据回归误差项的非参数密度估计的一致相合性(英文)

回归误差项是不可观测的. 由于回归误差项的密度函数在实际中有许多应用, 故使用非参数方法对其进行估计就成为回归分析中的一个基本问题. 针对完全观测数据回归模型, 曾有作者对此问题进行了研究. 然而在实际应用中, 经常会有数据被删失的情况发生, 在此情况下, 可以利用删失回归残差, 并使用核估计的方法对回归误差项的密度函数进行估计. 本文研究了该估计的大样本性质, 并证明了估计量的一致相合性.     

δ冲击模型中截尾数据的统计推断

本文研究了δ-冲击模型中参数δ的统计推断问题，该模型具有参数为λ的Poisson冲击，系统在当两个连续的冲击时间间隔小于δ时失效，失效的时间记为T．首先，我们给出了在δ小于平均冲击间隔时间(即1／λ)的情况下，失效时间T的密度函数的性质；然后我们给出了截尾数据的损失信息补偿的方法；借助Class-K方法，给出了δ的无偏、一致估计以和区间估计．最后，由Edgeworth展开和Boostrap方法，我们得到了δ的精确度更高的区间估计．