R: Plug-in Bandwidth Selectors for Kernel CDF Estimation

bw.CDF.pi {sROC} | R Documentation

## 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.

### Details

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

### Value

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

### Author(s)

X.F. Wang wangx6@ccf.org

### 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")

[Package sROC version 0.1-2 Index]