On the mean squared error of nonparametric quantile estimators under random right-censorship. (English) Zbl 0633.62033
Denote the well-known product limit estimator by \(\hat F_ n\), and the corresponding quantile function by \(\hat Q_ n(p)=\inf \{t\); \(\hat F{}_ n(t)\geq p\}\). The kernel type empirical quantile function studied by the second author [J. Am. Stat. Assoc. 81, 215-222 (1986; Zbl 0596.62043)] is defined as
\[
Q_ n(p)=h^{-1}\int^{1}_{0}\hat Q_ n(t)K((t-p)/h)dt
\]
for a kernel function K and bandwidth h. The authors study and compare the mean square errors of these two quantile estimators.
Reviewer: A.Földes
Keywords:
survival times; Kaplan-Meier estimator; randomly right-censored data; new asymptotic expressions; product limit estimator; kernel type empirical quantile function; mean square errors; quantile estimatorsCitations:
Zbl 0596.62043References:
[1] | DOI: 10.1016/0047-259X(85)90033-8 · Zbl 0577.62042 · doi:10.1016/0047-259X(85)90033-8 |
[2] | Cheng K.F., Sankhya 46 pp 426– (1984) |
[3] | Csörgo M., CBMS-NSF Regional Conference Series in Applied Mathematics (1983) |
[4] | Efron B., Proceedings of the Fifth Berkeley Symposium 4 pp 831– (1967) |
[5] | DOI: 10.1214/aos/1176346405 · Zbl 0533.62040 · doi:10.1214/aos/1176346405 |
[6] | DOI: 10.1214/aos/1176346605 · Zbl 0567.62035 · doi:10.1214/aos/1176346605 |
[7] | Földes A., Zeitschrift fur Wahrscheinlichkeitstheorie und Verwande Gebiete 56 pp 76– (1981) |
[8] | DOI: 10.2307/2281868 · Zbl 0089.14801 · doi:10.2307/2281868 |
[9] | Lio Y.L., Statistics and Probability Letters 53 (1986) |
[10] | DOI: 10.1016/0378-3758(86)90154-0 · Zbl 0608.62048 · doi:10.1016/0378-3758(86)90154-0 |
[11] | DOI: 10.2307/2287993 · Zbl 0596.62043 · doi:10.2307/2287993 |
[12] | DOI: 10.1080/03610918608812558 · Zbl 0609.62060 · doi:10.1080/03610918608812558 |
[13] | DOI: 10.2307/2286734 · Zbl 0407.62001 · doi:10.2307/2286734 |
[14] | Sander J., The Weak Convergence of Quantiles of the Product Limit Estimator (1975) |
[15] | DOI: 10.2307/2288567 · Zbl 0593.62037 · doi:10.2307/2288567 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.