Computes the plug-in bandwidth of Polansky and Baker.

Description

The bandwidth parameter for the distribution function kernel estimator is calculated, using the plug-in method of Polansky and Baker (2000). Four possible kernel functions can be used for the kernel estimator: "e" Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight. Because kernel estimators of derivatives of order bigger than two are required, only the normal kernel is used in this case.

Usage

PBbw(type_kernel = "n", vec_data, num_stage = 2)

Arguments

Value

A real value for the bandwidth parameter.

Author(s)

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

References

Polansky, A.M. and Baker, E.R. (2000) Multistage plug-in bandwidth selection for kernel distribution function estimates, Journal of Statistical Computation and Simulation 65, pp. 63-80.

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 plug-in bandwidth for a sample of 100 random N(0,1) data
x<-rnorm(100,0,1)
h_PB<-PBbw(vec_data=x,num_stage=4)
h_PB
## Not run: 
## A Quick plot of a distribution function estimate
x<-rnorm(1000)
h_PB<-PBbw(vec_data=x)
F_PB<-kde(vec_data=x, bw=h_PB)
plot(F_PB$grid, F_PB$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 the estimated
# distribution function
n_pts <- 100  
y <- seq(ss[1],ss[2],length.out=n_pts)
F_PB <- kde(type_kernel="e", x, y, h_PB)$Estimated_values
##  plot of the theoretical and estimated distribution functions
require(graphics)
plot(y,F_PB, type="l", lty=2)
lines(y, pnorm(y),type="l", lty=1)
legend(-1.2,0.8,c("real","nonparametric"),lty=1:2)

## End(Not run)

Results