| CI.CDF {sROC} | R Documentation |
Estimate the pointwise confidence intervals for Kernel Smooth CDF.
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.
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")