Acta Mathematicae Applicatae Sinica

, Volume 21, Issue 2, pp 311–322

Sequential Confidence Bands for Quantile Densities Under Truncated and Censored Data

Original Papers

DOI: 10.1007/s10255-005-0239-6

Cite this article as:
Zhou, Y. & Sun, L. Acta Mathematicae Applicatae Sinica, English Series (2005) 21: 311. doi:10.1007/s10255-005-0239-6
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Abstract

In this paper an asymptotic distribution is obtained for the maximal deviation between the kernel quantile density estimator and the quantile density when the data are subject to random left truncation and right censorship. Based on this result we propose a fully sequential procedure for constructing a fixed-width confidence band for the quantile density on a finite interval and show that the procedure has the desired coverage probability asymptotically as the width of the band approaches zero.

Keywords

Truncated and censored dataquantile density estimationmaximal deviationasymptotic distributionsequential confidence band

2000 MR Subject Classification

62G0562E20

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100080China