We analyze left-truncated and right-censored data using Cox proportional hazard models with long-term survivors. The estimators of covariate coefficients and the long-term survivor proportion are obtained by the parti...We analyze left-truncated and right-censored data using Cox proportional hazard models with long-term survivors. The estimators of covariate coefficients and the long-term survivor proportion are obtained by the partial likelihood method, and their asymptotic properties are also established. Simulation studies demonstrate the performance of the proposed estimators, and an application to a real dataset is provided.展开更多
For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n...For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.展开更多
For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are stro...For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.展开更多
This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival...This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.展开更多
In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right cens...In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.展开更多
基金Natural Science Funds for Distinguished Young Scholar (No. 70825004)Creative Research Groups of China (No. 10721101)+2 种基金Shanghai University of Finance and Economics Project 211 Phase ⅢShanghai Leading Academic Discipline Project (No. B803)Zhou's work was supported by Graduate Creation Funds of Shanghai University of Finance and Economics(No. CXJJ-2011-436)
文摘We analyze left-truncated and right-censored data using Cox proportional hazard models with long-term survivors. The estimators of covariate coefficients and the long-term survivor proportion are obtained by the partial likelihood method, and their asymptotic properties are also established. Simulation studies demonstrate the performance of the proposed estimators, and an application to a real dataset is provided.
基金the National Natural Science Foundation of China (Grant No. 19971006) .
文摘For left truncated and right censored model, letF n be the product-limit estimate and φ a nonnegative measurable function. The almost sure limits of the cumulative hazard function based onF n pd the integral ∫ ?dF n are given. The results are useful in establishing strong consistent results of various estimates. For left truncated data, similar results were obtained in literature.
文摘For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.
文摘This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component’s reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.
文摘In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.
