An empirical estimate of quantile density function in presence of censoring

Abstract

In survival or reliability studies, the quantile density function is an important characteristic in understanding the survival or aging process. In this various types of studies, a typical problem encountered in the data collection stage is that the samples may be censored from the right. In this article, we consider the problem of nonparametric estimation of a quantile density with right-censored data. A new adaptive wavelet estimator of this function is defined and its asymptotic properties are studied. In order to evaluate the performance of our estimator, small Monte Carlo simulations are carried out. Results show that the proposed estimators work well especially when the sample size is small and their calculations are simple. Finally, a real data example is provided.

Keywords:

• Adaptivity
• threshold estimator
• right censored data
• quantile density
• wavelets

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62G07
• 62G20

Data availability

The Channing House data employed in this article is available in the package “boot” of R.

Acknowledgements

The author would like to sincerely thank the editor, associate editor and two anonymous referees for their constructive comments, which helped me to improve the manuscript.

Funding

This work was supported by Ministry of Science and Technology, Taiwan [Grant ID MOST 109-2118-M-032 -001 -MY2].

Additional information

Funding

The author was supported by Grant University of Gonbad Kavous with No. 6.253.