ALbw: Compute the Plug-in Bandwidth of Altman and Leger

In kerdiest: Nonparametric Kernel Estimation of Distribution Function

Compute 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.

Value

A numeric value for the bandwidth parameter.

Author(s)

Graciela Estévez Pérez and Alejandro Quintela del Río

References

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

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_AL <- ALbw(type_kernel = "e", vec_data = x)
h_AL

## 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")
## 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
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)

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