R: Kernel Estimation for Cumulative Distribution Function

kCDF {sROC} | R Documentation

## Kernel Estimation for Cumulative Distribution Function

### Description

To compute the nonparametric kernel estimate for cumulative distribution function (CDF).

### Usage

    kCDF(x, bw="pi_ucv", adjust=1, kernel=c("normal", "epanechnikov"), xgrid,
    	ngrid=256, from, to, cut=3, na.rm = FALSE, ...)

### Arguments

`x` | the data from which the estimate is to be computed.
`bw` | the smoothing bandwidth to be used. `bw` can also be a character string giving a rule to choose the bandwidth. See `bw.CDF` and `bw.CDF.pi`. The default used the Altman and Leger's plug-in approach with an unbiased cross-validation pilot bandwidth.
`adjust` | the parameter for adjusting the bandwidth. The bandwidth used for the estimate is actually `adjust*bw`. By default, adjust=1.
`kernel` | a character string giving the smoothing kernel to be used. This must be either “normal” or “epanechnikov”. By default, the normal kernel is used.
`xgrid` | the user-defined data points at which the CDF is to be evaluated. If missing, the CDF will be evaluated at the equally spaced points defined within the function.
`ngrid` | the number of equally spaced points at which the density is to be estimated.
`from` | the left-most points of the grid at which the density is to be estimated.
`to` | the right-most points of the grid at which the density is to be estimated
`cut` | by default, the values of from and to are cut bandwidths beyond the extremes of the data.
`na.rm` | logical; if `TRUE`, missing values are removed from x. If `FALSE` any missing values cause an error.
`...` | further arguments for methods.

### Details

estimate the nonparametric kernel cumulative distribution function.

### Value

An object of class “CDF”.

`x` | the points where the CDF is estimated.
`Fhat` | the estimated CDF values. These will be numerical numbers between zero and one.
`bw` | the bandwidth used.
`n` | the sample size after elimination of missing values.
`call` | the call which produced the result.
`data` | the original data after elimination of missing values.
`data.name` | the deparsed name of the `x` argument.
`has.na` | logical; if `TRUE`, there are missing values in the original data.

The `print` method reports `summary` values on the `x` and `Fhat` components.

### Author(s)

X.F. Wang wangx6@ccf.org

### References

Nadaraya, E.A. (1964). Some new estimators for distribution functions. Theory of Probability and its Applications, 9, 497-500.

Altman, N., and Leger, C. (1995). Bandwidth selection for kernel distribution function estimation. Journal of Statistical Planning and Inference, 46, 195-214.

### See Also

`bw.CDF`, `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
    plot(x.CDF, alpha=0.05, main="Kernel estimate of distribution function", CI=FALSE)
    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]