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

## Description

Estimate the pointwise confidence intervals for Kernel Smooth CDF.

## Usage

 `1` ``` CI.CDF(CDF, alpha=0.05) ```

## Arguments

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

## Details

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

## Value

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.

## Author(s)

X.F. Wang wangx6@ccf.org

## References

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`.
 ```1 2 3 4 5 6 7 8``` ```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") ```