Asymptotically optimal bandwidth for a smooth nonparametric quantile estimator under censoring

Abstract

Based on randomly right-censored data, define the smooth quantile estimator,ξ_p 0<p < 1, to be the solution to F _nξ=p, where F _n is the distribution function corresponding to a kernel estimator of the lifetime density. It is shown that the bandwidth h ₀ = Cn ^-1/(2k-1) for k≧2 is asymptotically optimal for ξ_p in a probability sense, where the constant C depends on p, the kernel function K, the lifetime density, the censoring distribution, and the order k of the kernel. For a second-order kernelk = 2h ₀ is of the order n ^-1/3, which is quite different from the optimal bandwidth for the kernel density estimator under censoring obtained by Marron and Padgett (1987).

Keywords:

• Quantile function
• kernel estimation
• bandwidth selection
• random right censorship
• survival analysis

Supported by General Research Minigrant of the University of South Dakota No. 202-4855-000.

Partially supported by U.S. Army Research Office under grant number DAAL-03-87-K-0101.

Supported by General Research Minigrant of the University of South Dakota No. 202-4855-000.

Partially supported by U.S. Army Research Office under grant number DAAL-03-87-K-0101.

Notes

Supported by General Research Minigrant of the University of South Dakota No. 202-4855-000.

Partially supported by U.S. Army Research Office under grant number DAAL-03-87-K-0101.