Abstract

We consider the nonparametric analysis of length-biased and right-censored data (LBRC) by quantile difference. With its desirable properties such as superior robustness and easy interpretation, quantile difference has been widely used in practice, in particular, for missing and survival data. Existing approaches for nonparametric estimation of quantile difference in length-biased survival data, however, exhibit some drawbacks such as non-smoothness and instabilities. To overcome these difficulties, we proposed a smoothed quantile difference estimation approach to improve its estimating efficiency with its validity justified by asymptotic theories. Simulations are also conducted to evaluate the performance of the proposed estimator. An application to the Channing house data is further provided for illustration.

摘要

我们考虑通过分位数差异对长度偏差和右删失数据 (LBRC) 进行非参数分析。分位数差异具有优异的鲁棒性和易于解释等理想特性，已在实践中得到广泛应用，特别是对于缺失数据和生存数据。然而，现有的对偏长生存数据的分位数差异进行非参数估计的方法存在一些缺点，例如不平滑和不稳定性。为了克服这些困难，我们提出了一种平滑的分位数差异估计方法，以提高其估计效率，其有效性由渐近理论证明。还进行了模拟以评估所提出的估计器的性能。为了说明，进一步提供了对钱宁屋数据的应用。