sROC (version 0.1-2)

CI.CDF: 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.

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.

Details

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

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")