kde: Kernel Estimation of the Distribution Function

In kerdiest: Nonparametric Kernel Estimation of Distribution Function

Kernel Estimation of the Distribution Function

Description

Computes the value of the kernel estimator of the distribution function, in a single value or in a grid. Four possibilites for the kernel function are implemented, and the bandwidth parameter can be directly calculated by the plug-in method of Polansky and Baker (2000).

Usage

kde(type_kernel = "n", vec_data, y = NULL,
           bw = PBbw(type_kernel = "n", vec_data, 2))

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.
y	The single value or the grid vector where the distribution function is estimated. By default, a grid of 100 equidistant points from the minimum to the maximum of the data sample is selected.
bw	The bandwidth used. If it is not provided, the plug-in bandwidth of Polansky and Baker (2000) is computed.

Value

A list containing:

Estimated_values	Vector containing the estimated function in the grid values.
grid	The used grid.
bw	Value of the bandwidth.

Author(s)

Graciela Estévez Pérez and Alejandro Quintela del Río

References

Reiss, R.D. (1981), "Nonparametric estimation of smooth distribution functions", Scandinavian Journal of Statistics, 8, 116-119.

Simonoff, J. (1996), "Smoothing Methods in Statistics", Springer, New York.

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

## Comparison of three bandwidth selection methods
x <- rnorm(100)
## The bandwidths by cross-validation, plug-in of Altman and Leger
## and plug-in of Polansky and Baker are computed using a normal kernel
## and a standard setting of parameters
h_CV <- CVbw(vec_data = x)$bw
h_CV
## Plug-in of Altman and Leger
h_AL <- ALbw(vec_data = x)
h_AL
## Plug-in of Polansky and Baker
h_PB <- PBbw(vec_data = x)
h_PB
## Plot of the three estimates together with the real distribution
F_CV <- kde(vec_data = x, bw = h_CV)
F_AL <- kde(vec_data = x, bw = h_AL)
F_PB <- kde(vec_data = x, bw = h_PB)
y <- F_CV$grid
Ft <- pnorm(y)
plot(y, Ft, ylab = "Distribution", xlab = "Data", type = "l", lty = 1)
lines(y, F_CV$Estimated_values, type = "l", lty = 2)
lines(y, F_AL$Estimated_values, type = "l", lty = 3)
lines(y, F_PB$Estimated_values, type = "l", lty = 4)
legend(1, 0.4, c("Real", "F_CV", "F_AL", "F_PB"), lty = 1:4)

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