CI.CDF: Pointwise Confidence Intervals for Kernel Smooth CDF
In sROC: Nonparametric Smooth ROC Curves for Continuous Data

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/sROC.R

Estimate the pointwise confidence intervals for Kernel Smooth CDF.

1	CI.CDF(CDF, alpha=0.05)

`CDF`	a “CDF” object generated by kCDF(...).
`alpha`	the significant level. The default is 0.05 which generates 95% confidence intervals for the CDF.

The pointwise confidence intervals are calculated by the asymptotic distribution of the kernel estimator of CDF.

A list contents

`x`	the points where the CDF is estimated.
`Fhat`	the estimated CDF values. These will be numerical numbers between zero and one.
`Fhat.upper`	the upper boundaries of the CDF.
`Fhat.lower`	the lower boundaries of the CDF.
`alpha`	the significant level used.

X.F. Wang wangx6@ccf.org

Azzalini, A. (1981). A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika, 68, 326-328.

Wang, X.F., Fan, Z., and Wang, B. (2010). Estimating smooth distribution function in the presence of heteroscedastic measurement errors. Computational Statistics and Data Analysis, 54(1), 25-36.

kCDF, bw.CDF.pi.

set.seed(100)
n <- 200
x <- c(rnorm(n/2, mean=-2, sd=1), rnorm(n/2, mean=3, sd=0.8))
x.CDF <- kCDF(x)
x.CDF
CI.CDF(x.CDF)
plot(x.CDF, alpha=0.05, main="Kernel estimate of distribution function")
curve(pnorm(x, mean=-2, sd=1)/2 + pnorm(x, mean=3, sd=0.8)/2, from =-6, to=6, add=TRUE, lty=2, col="blue")