PBbw: Compute the Plug-in Bandwidth of Polansky and Baker

In kerdiest: Nonparametric Kernel Estimation of Distribution Function

Compute 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 greater than two are required, only the normal kernel is used in this case.

Usage

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

Arguments

type_kernel	The kernel function used. 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.
num_stage	The number of iterations in the Polansky and Baker method. The default, 2, is usually a good option. Values of 3 or 4 are also allowed.

Value

A numeric value for the bandwidth parameter.

Author(s)

Graciela Estévez Pérez and Alejandro Quintela del Río

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, 63-80.

Quintela-del-Río, A. and Estévez-Pérez, G. (2012), "Nonparametric kernel distribution function estimation with kerdiest: an R package for bandwidth choice and applications", Journal of Statistical Software, 50(8), 1-21.

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

## 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")
## 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
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)

kerdiest documentation built on June 23, 2025, 5:08 p.m.