sROC (version 0.1-2)

bw.CDF.pi: Plug-in Bandwidth Selectors for Kernel CDF Estimation

Description

Plug-in bandwidth selectors for kernel CDF estimation using Altman and Leger's approach.

Usage

bw.CDF.pi(x, pilot="UCV")

Arguments

x

numeric vector.

pilot

a character string giving a rule to choose the pilot bandwidth to estimate $E(f''(x))$. There are 6 choices: The default, ``ucv'', implement unbiased cross-validation, ``nrd0'' is the Silverman's rule of thumb, ``nrd'' is the Scott's method (1992), ``bcv'' is the biased cross-validation, ``sj'' is the method of Sheather and Jones (1991), ``onestage'' is the one-stage method by Wand and Jones.

Value

A bandwidth on a scale suitable for the bw argument of kCDF.

Details

bw.CDF implements a rule-of-thumb for choosing the bandwidth of a Gaussian kernel CDF estimator.

References

Altman, N., and Leger, C. (1995). Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference, 46, 195-214.

Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of Royal Statistical Society Series B, 53, 683-690.

Silverman, B. W. (1986) Density Estimation. London: Chapman and Hall.

Wand, M.P. and Jones, M.C. (1995) Kernel Smoothing. New York: Chapmon and Hall.

See Also

kCDF, bw.CDF.

Examples

set.seed(100)
n <- 200
x <- c(rnorm(n/2, mean=-2, sd=1), rnorm(n/2, mean=3, sd=0.8))
bw.CDF.pi(x)
bw.CDF.pi(x, pilot="nrd0")
bw.CDF.pi(x, pilot="nrd")
bw.CDF.pi(x, pilot="bcv")
bw.CDF.pi(x, pilot="sj")
bw.CDF.pi(x, pilot="onestage")