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Last data update: 2014.03.03

R: Computes the cross-validation bandwidth of Bowman et al...

CVbw	R Documentation

Computes the cross-validation bandwidth of Bowman et al (1998).

Description

The bandwidth parameter for the distribution function kernel estimator is calculated, using the modified cross-validation method of Bowman, Hall and Prvan (1998). Four possible kernel functions can be used: "e" Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight. The cross-validation function involves an integral term, that is calculated using the Simpson's rule.

Usage

CVbw(type_kernel = "n", vec_data, n_pts = 100, seq_bws =NULL)

Arguments

`type_kernel`	The kernel function. You can use four types: "e" Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight. The normal kernel is used by default.
`vec_data`	The data sample.
`n_pts`	The number of points used to approximate, by the Simpson's rule, the integral term, in the cross-validation function. Because this numeric method enlarge the computing time, you can check different numbers, depending on your sample size. 100 points are used by default.
`seq_bws`	The sequence of bandwidths in which to compute the cross-validation function. By default, the procedure defines a sequence of 50 points, from the range of the data divided by 200 to the range divided by 2.

Value

A list consisting of

`seq_bws`	The sequence of bandwidths.
`CV function`	The values of the cross-validation function in the bandwidths grid.
`bw`	A real value for the cross-validation bandwidth.

Author(s)

Graciela Estevez Perez graci@udc.es and Alejandro Quintela del Rio aquintela@udc.es

References

Bowman, A.W., Hall, P. and Prvan,T. (1998) Cross-validation for the smoothing of distribution functions, Biometrika 85, pp. 799-808.

Quintela-del-Rio, A. and Estevez-Perez, G. (2012) Nonparametric Kernel Distribution Function Estimation with kerdiest: An R Package for Bandwidth Choice and Applications, Journal of Statistical Software 50(8), pp. 1-21. URL http://www.jstatsoft.org/v50/i08/.

Examples

##  Compute the cross-validation bandwidth for a sample of 100 random N(0,1) data
x<-rnorm(100,0,1)
num_bws <- 50
seq_bws <- seq(((max(x)-min(x))/2)/50,(max(x)-min(x))/2,length=num_bws) 
hCV <- CVbw(type_kernel="e", vec_data=x, n_pts=200, seq_bws=seq_bws)
hCV
##  The CV function is plotted
h_CV<-CVbw(vec_data=x)
h_CV$bw
plot(h_CV$seq_bws, h_CV$CVfunction, type="l")
## Not run: 
##  Plotting the distribution function estimate controling the grid points 
## and the kernel function
ss <- quantile(x, c(0.05, 0.95))
# number of points to be used in the representation of estimated distribution
# function
n_pts <- 100  
y <- seq(ss[1],ss[2],length.out=n_pts)
F_CV<-kde(type_kernel="e", x, y, h_CV$bw)$Estimated_values
##  plot of the theoretical and estimated distribution functions
require(graphics)
plot(y,F_CV, type="l", lty=2)
lines(y, pnorm(y),type="l", lty=1)
legend(-1,0.8,c("real","nonparametric"),lty=1:2)

## End(Not run)