×

Relative deficiency of kernel type estimators of quantiles based on right censored data. (English) Zbl 0724.62048

Summary: The problem of estimating the smooth quantile function Q(\(\cdot)\) at a fixed point p, \(0<p<1\), is treated under a nonparametric smoothness condition on Q. The asymptotic relative deficiency of product-limit quantile with respect to kernel type estimators of the quantile is evaluated. The comparison is based on the mean square errors of the estimators. It is shown that the relative deficiency tends to infinity as the sample size n tends to infinity.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/0047-259X(85)90033-8 · Zbl 0577.62042 · doi:10.1016/0047-259X(85)90033-8
[2] Cheng K. F., Sankhyā Ser, A, 46 pp 428– (1984)
[3] Csörgó M., Quantile Processes with Statistical Applications. CMBS-NSF Regional Conference Series in Applied Mathematics. (1983)
[4] DOI: 10.1214/aos/1176342410 · Zbl 0258.62032 · doi:10.1214/aos/1176342410
[5] DOI: 10.1214/aos/1176346405 · Zbl 0533.62040 · doi:10.1214/aos/1176346405
[6] Gardiner J., Adaptive Statistical Procedures and Related Topics, IMS Lecture Notes. 8 pp 350– (1985)
[7] DOI: 10.1016/0378-3758(88)90002-X · Zbl 0641.62025 · doi:10.1016/0378-3758(88)90002-X
[8] DOI: 10.2307/2281868 · Zbl 0089.14801 · doi:10.2307/2281868
[9] DOI: 10.1080/03610928708829458 · Zbl 0633.62033 · doi:10.1080/03610928708829458
[10] DOI: 10.1016/0378-3758(86)90154-0 · Zbl 0608.62048 · doi:10.1016/0378-3758(86)90154-0
[11] DOI: 10.1007/BF01000216 · Zbl 0561.62032 · doi:10.1007/BF01000216
[12] DOI: 10.1214/aos/1176346582 · Zbl 0575.62043 · doi:10.1214/aos/1176346582
[13] DOI: 10.2307/2287993 · Zbl 0596.62043 · doi:10.2307/2287993
[14] Sander, J. M. 1975. ”The weak convergence of quantiles of the product-limit estimator”. Standford University. Technical Report 5, Division of Biostatistics
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.