R: Computes the plug-in bandwidth of Altman and Leger.
ALbw
R Documentation
Computes the plug-in bandwidth of Altman and Leger.
Description
The bandwidth parameter for the distribution function kernel
estimator is calculated, using the plug-in method of Altman and Leger (1995).
Four possible kernel functions can be used for the kernel estimator: "e"
Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight.
Usage
ALbw(type_kernel = "n", vec_data)
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.
Details
Altman and Leger (1995) recommend the use of the Epanechnikov kernel, because
in this case the rate of convergence for the kernel derivative estimator is
improved. For the sake of uniformity along the package, the gaussian kernel is
used by default, but the user can obviously choose the Epanechnikov function.
Altman, N., Leger, C. (1995) Bandwidth selection for kernel distribution
function estimation. Journal of Statistical Planning and Inference46, pp. 195–214.
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 Software50(8), pp. 1-21.
URL http://www.jstatsoft.org/v50/i08/.
Examples
# Compute the plug-in bandwidth for a sample of 100 random N(0,1) data
x<-rnorm(100,0,1)
h_AL<- ALbw(type_kernel="e",vec_data=x)
h_AL
## Not run:
## A Quick plot of a distribution function estimate
x<-rnorm(1000)
h_AL<-ALbw(vec_data=x)
F_AL<-kde(vec_data=x, bw=h_AL)
plot(F_AL$grid,F_AL$Estimated_values,type="l")
## End(Not run)
## 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_AL <- kde(type_kernel="e", x, y, h_AL)$Estimated_values
## plot of the theoretical and estimated distribution functions
require(graphics)
plot(y,F_AL, 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)