Nonparametric smoothed quantile difference estimation for length-biased and right-censored data

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.

Keywords:

• Bias sampling
• length-biased data
• quantile difference
• right-censored data
• smoothing estimation

Additional information

Funding

Shi’s work is supported by the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics, the Overseas Project of Minnan Normal University, Natural Science Foundation of Fujian Province (2019Y3007), China. Liu’s work is supported by the Fundamental Research Funds for the Central Universities (QL 18009), and Foundation of Central University of Finance and Economics (CUFE) (CUFESAM201811), and the disciplinary funding of CUFE(SAM201912), National Natural Science Foundation of China (11401603). Xu’s work was supported by the University of Hong Kong, Zhejiang Institute of Research and Innovation Seed Fund and the Hong Kong General Research Fund (17308018,17306619).