共查询到20条相似文献,搜索用时 31 毫秒
1.
An alternative to the accelerated failure time model is to regress the median of the failure time on the covariates. In the recent years, censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. Based on missing information principle, a semiparametric inference procedure for regression parameter has been developed when censoring variable depends on continuous covariate. In order to improve the low coverage accuracy of such procedure, we apply an empirical likelihood ratio method (EL) to the model and derive the limiting distributions of the estimated and adjusted empirical likelihood ratios for the vector of regression parameter. Two kinds of EL confidence regions for the unknown vector of regression parameters are obtained accordingly. We conduct an extensive simulation study to compare the performance of the proposed methods with that normal approximation based method. The simulation results suggest that the EL methods outperform the normal approximation based method in terms of coverage probability. Finally, we make some discussions about our methods. 相似文献
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Recent advances in median regression model have made it possible to use this model for analyzing a variety of censored survival data. For inference on the model parameter vector, there are now semiparametric procedures based on normal approximation that are valid without strong conditions on the error distribution. However, the accuracy of such procedures can be quite low when the censoring proportion is high. In this paper, we propose an alternative semiparametric procedure based on the empirical likelihood. We define the empirical likelihood ratio for the parameter vector and show that its limiting distribution is a weighted sum of chi-square distributions. Numerical results from a simulation study suggest that the empirical likelihood method is more accurate than the normal approximation based method of Ying et al. (J. Amer. Statist. Assoc. 90 (1995) 178). 相似文献
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Yichuan Zhao 《Journal of multivariate analysis》2010,101(8):1846-1858
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. 相似文献
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Yichuan Zhao 《Statistics & probability letters》2011,81(5):603-610
Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method. 相似文献
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In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test.Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy.In this paper,empirical likelihood (EL) method is proposed for the AUC regression model.For the regression parameter vector,it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions.Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem,as well as for the covariate-specific AUC.Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression.Finally,the proposed methods are illustrated with a real data set. 相似文献
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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. 相似文献
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We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies. 相似文献
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针对响应变量缺失下的半参数回归模型,构造模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近χ2分布,由此构造未知参数的置信域,并就置信域的覆盖概率及区间长度方面,通过模拟研究与最小二乘法进行优劣比较. 相似文献
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This paper develops the empirical likelihood (EL) inference on parameters and baseline function in a semiparametric nonlinear regression model for longitudinal data in the presence of missing response variables. We propose two EL-based ratio statistics for regression coefficients by introducing the working covariance matrix and a residual-adjusted EL ratio statistic for baseline function. We establish asymptotic properties of the EL estimators for regression coefficients and baseline function. Simulation studies are used to investigate the finite sample performance of our proposed EL methodologies. An AIDS clinical trial data set is used to illustrate our proposed methodologies. 相似文献
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Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method. 相似文献
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In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d. observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results. 相似文献
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该文考虑非线性半参数回归模型,构造了模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近Χ2分布,由此结果可以用来构造未知参数的置信域.另外,该文也构造了未知参数 的最小二乘估计量,并证明了它的渐近性质.仅就置信域精度及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣. 相似文献
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This paper is focused on testing the parameters of the quantile regression models. For complete observation, it is shown in literature that the test statistics, based on empirical likelihood (EL) method and smoothed empirical likelihood (SEL) method, both converge weakly to the standard Chi-square distribution $\chi_M^2$ under the null hypothesis. For right censored data, the statistics in literature, by the EL method, have a weighted Chi-square limiting distribution, but the weights are unknown. In this paper, we show that the statistics based on the EL method and the SEL method also converge weakly to $\chi_M^2$
under the null hypothesis, so there is no need to estimate any weights. As its estimating function is smoothed, the SEL method can be Bartlett corrected. Numerical results show that the SEL method, via Bartlett correction, outperforms some recent methods. 相似文献
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Empirical likelihood for single-index models 总被引:1,自引:0,他引:1
The empirical likelihood method is especially useful for constructing confidence intervals or regions of the parameter of interest. This method has been extensively applied to linear regression and generalized linear regression models. In this paper, the empirical likelihood method for single-index regression models is studied. An estimated empirical log-likelihood approach to construct the confidence region of the regression parameter is developed. An adjusted empirical log-likelihood ratio is proved to be asymptotically standard chi-square. A simulation study indicates that compared with a normal approximation-based approach, the proposed method described herein works better in terms of coverage probabilities and areas (lengths) of confidence regions (intervals). 相似文献
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In this article we study the empirical likelihood inference for MA(q) model. We propose the moment restrictions, by which we get the empirical likelihood estimator of the model parameter, and we also propose an empirical log-likelihood ratio based on this estimator. Our result shows that the EL estimator is asymptotically normal, and the empirical log-likelihood ratio is proved to be asymptotical standard chi-square distribution. 相似文献