R: Pointwise Confidence Intervals for Kernel Smooth CDF

CI.CDF {sROC} | R Documentation

## Pointwise Confidence Intervals for Kernel Smooth CDF

### Description

Estimate the pointwise confidence intervals for Kernel Smooth CDF.

### Usage

     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.

### See Also

`kCDF`, `bw.CDF.pi`.

### Examples

    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")

[Package sROC version 0.1-2 Index]