区间数据均值的经验似然估计

本文提出了估计区间数据均值的经验似然方法,通过构造区间数据的无偏转换,导出了渐近服从χ2分布的对数经验似然函数,从而得到了均值的置信区间.通过若干模拟例子说明,用本文提出的方法得到的估计,优于用渐近正态法得到的估计.     

区间数据情形下线性模型的经验似然推断

§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…     

右删失数据下非线性回归模型的经验似然推断

考虑随机右删失数据下非线性回归模型,提出了模型中未知参数的调整的经验对数似然比统计量.在一定的条件下,证明了.所提出的的统计量具有渐近χ~2分布,由此结果构造了兴趣参数的置信域.通过模拟研究,对经典的经验似然、调整的经验似然和非线性最小二乘方法在有限样本下进行了比较,并对氯离子浓度试验数据进行了分析.     

核实数据下响应变量缺失的线性EV模型经验似然推断

考虑响应变量随机缺失而协变量带有误差的线性模型,借助于核实数据和借补方法,构造了回归系数的两种经验似然比,证明了所提出的估计的经验对数似然比渐近于一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整经验对数似然比渐近于自由度为p的χ2分布,该结果可以用来构造未知参数的置信域.此外,我们也构造了响应均值的调整经验对数似然比统计量,并证明了所提出的统计量渐近于x2分布,可用此结果构造响应均值的置信域.通过模拟研究比较了置信域的精度及其平均区间长度.     

具有随机右删失随机变量分位数的经验似然推断

本文研究了具有随机右删失随机变量分位数的置信域的构造.利用经验似然和截尾值估算相结合的方法,给出了分位数的对数经验似然比统计量,在较少的条件下证明了该统计量的极限分布为自由度为1的x~2分布.使得完全数据下的分位数的经验似然推断方法应用到非完全数据中.     

基于截尾数据指数Pareto分布应力-强度模型的可靠性

在II型双截尾删失计划下，讨论了当系统被独立的随机施加指数Pareto （EP）压力时的系统可靠性问题.作者给出了系统可靠性参数的不同点估计和区间估计，其中点估计包括一致最小方差无偏估计（UMVUE）和最大似然估计（MLE）；区间估计包括精确置信区间，近似置信区间和bootstrap的区间估计.为了评价不同估计方法效果，作者提供数值模拟结果；最后提供了一个真实数据的分析结果来演示本文提出的方法.     

Statistical Analysis of Series System for Masked Data under Successive Censored Life Test

In this paper, considering series system of masked data under simple successive censored and multiple successive censored life test, the likelihood function and maximum likelihood estimate are respectively proposed for series system composed of two units under two kinds of situations. One is the series system composed of two units with constant failure rate, and the other is the series system composed of two units with linear failure rate through the origin. The approximate interval estimates of parameters are given by using the method of likelihood ratio. Besides, the examples show the feasibility of the methods through Monte-Carlo simulations.     

Empirical likelihood for the contrast of two hazard functions with right censoring

In this paper, we consider the standard two-sample framework with right censoring. We construct useful confidence intervals for the ratio or difference of two hazard functions using smoothed empirical likelihood (EL) methods. The empirical log-likelihood ratio is derived and its asymptotic distribution is a standard chi-squared distribution. Bootstrap confidence bands are also proposed. Simulation studies show that the proposed EL confidence intervals have outperformed normal approximation methods in terms of coverage probability. It is concluded that the empirical likelihood methods provide better inference results.     

Inference for constant-stress accelerated degradation test based on Gamma process

This paper proposes a Gamma constant-stress accelerated degradation model based on the principle of the degradation mechanism invariance. The maximum likelihood estimators of the parameters of the proposed model are derived. Based on Cornish–Fisher expansion, the approximate confidence interval for the shape parameter of the Gamma degradation process is developed. Since it is difficult to obtain the exact confidence intervals for other model parameters and some quantities such as the mean degradation in unit time, the quantile and the reliability function of the lifetime at the normal stress level, the generalized confidence intervals for these quantities are proposed. The percentiles of the proposed generalized pivotal quantities can be obtained by the simulation. The performances of the proposed confidence intervals are evaluated by the Monte Carlo simulation method. In the simulation study, the proposed confidence intervals are compared with the Wald and the bootstrap-p confidence intervals. The simulation results show that the proposed confidence intervals outperform the Wald and the bootstrap-p confidence intervals in terms of the coverage percentage. Finally, a real example is used to illustrate the proposed procedures.     

截断情况下线性回归模型响应变量均值的经验似然

本文讨论了在带有截断情况的线性回归模型中 ,响应变量均值的估计问题 .将经验似然的方法应用到带有截断情况的回归模型中 ,在估计响应变量的均值时构造了调整的经验似然统计量 ,证明了在一定的条件下 ,该统计量渐近服从 χ2 分布 ,给出了均值的置信区间 ,并与正态下得到的结果进行了比较 ,模拟的结果说明了经验似然的优良性 .     

Empirical likelihood analysis of the Buckley-James estimator

The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429-436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley-James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley-James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley-James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies.     

响应变量删失情况下线性模型的FIC模型选择和模型平均

本文给出了响应变量随机右删失情况下线性模型的FIC (focused information criterion) 模型选择方法和光滑FIC 模型平均估计方法, 证明了兴趣参数的FIC 模型选择估计和光滑FIC 模型平均估计的渐近正态性, 通过随机模拟研究了估计的有限样本性质, 模拟结果显示, 从均方误差和一定置信水平置信区间的经验覆盖概率看, 兴趣参数的光滑FIC 模型平均估计均优于FIC, AIC (Akaikeinformation criterion) 和BIC (Bayesian information citerion) 等模型选择估计; 而FIC 模型选择估计与AIC 和BIC 等模型选择估计相比, 也表现出了一定的优越性. 通过分析原发性胆汁性肝硬化数据集, 说明了本文方法在实际问题中的应用.     

核实数据下删失线性EV模型的经验似然推断

本文考虑协变量带有误差的删失线性回归模型,借助于核实数据,对回归系数构造了两种经验对数似然比统计量,证明了所提出的估计的经验对数似然比统计量渐近收敛到一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整的经验对数似然比统计量具有渐近标准χ2p分布,所得结果可以用来构造未知参数的置信域,通过模拟研究在置信域的精度及其平均区间长度大小方面进行了比较。     

An empirical likelihood method in a partially linear single-index model with right censored data

Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard χ2-limit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.     

A New Approach to Censored Quantile Regression Estimation

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.     

Model-based likelihood ratio confidence intervals for survival functions

We introduce an adjusted likelihood ratio procedure for computing pointwise confidence intervals for survival functions from censored data. The test statistic, scaled by a ratio of two variance quantities, is shown to converge to a chi-squared distribution with one degree of freedom. The confidence intervals are seen to be a neighborhood of a semiparametric survival function estimator and are shown to have correct empirical coverage. Numerical studies also indicate that the proposed intervals have smaller estimated mean lengths in comparison to the ones that are produced as a neighborhood of the Kaplan-Meier estimator. We illustrate our method using a lung cancer data set.     

Semiparametric inference for transformation models via empirical likelihood

Recent advances in the transformation model have made it possible to use this model for analyzing a variety of censored survival data. For inference on the regression parameters, there are semiparametric procedures based on the normal approximation. However, the accuracy of such procedures can be quite low when the censoring rate is heavy. In this paper, we apply an empirical likelihood ratio method and derive its limiting distribution via U-statistics. We obtain confidence regions for the regression parameters and compare the proposed method with the normal approximation based method in terms of coverage probability. The simulation results demonstrate that the proposed empirical likelihood method overcomes the under-coverage problem substantially and outperforms the normal approximation based method. The proposed method is illustrated with a real data example. Finally, our method can be applied to general U-statistic type estimating equations.     

删失数据下变系数部分线性模型的经验似然变量选择

In this paper, we consider the variable selection for the parametric components of varying coefficient partially linear models with censored data. By constructing a penalized auxiliary vector ingeniously, we propose an empirical likelihood based variable selection procedure, and show that it is consistent and satisfies the sparsity. The simulation studies show that the proposed variable selection method is workable.     

Empirical Likelihood Ratio With Arbitrarily Censored/Truncated Data by EM Algorithm

The empirical likelihood is a general nonparametric inference procedure with many desirable properties. Recently, theoretical results for empirical likelihood with certain censored/truncated data have been developed. However, the computation of empirical likelihood ratios with censored/truncated data is often nontrivial. This article proposes a modified self-consistent/EM algorithm to compute a class of empirical likelihood ratios for arbitrarily censored/truncated data with a mean type constraint. Simulations show that the chi-square approximations of the log-empirical likelihood ratio perform well. Examples and simulations are given in the following cases: (1) right-censored data with a mean parameter; and (2) left-truncated and right-censored data with a mean type parameter.     

Empirical likelihood for mixed-effects error-in-variables model

This paper mainly introduces the method of empirical likelihood and its applications on two different models. We discuss the empirical likelihood inference on fixed-effect parameter in mixed-effects model with error-in-variables. We first consider a linear mixed-effects model with measurement errors in both fixed and random effects. We construct the empirical likelihood confidence regions for the fixed-effects parameters and the mean parameters of random-effects. The limiting distribution of the empirical log likelihood ratio at the true parameter is X2p＋q, where p, q are dimension of fixed and random effects respectively. Then we discuss empirical likelihood inference in a semi-linear error-in-variable mixed-effects model. Under certain conditions, it is shown that the empirical log likelihood ratio at the true parameter also converges to X2p＋q. Simulations illustrate that the proposed confidence region has a coverage probability more closer to the nominal level than normal approximation based confidence region.