kerdiest (version 1.3-1)

CVbw: Compute the Cross-Validation Bandwidth of Bowman et al (1998)

Description

The bandwidth parameter for the distribution function kernel estimator is calculated using the modified cross-validation method of Bowman, Hall and Prvan (1998). Four possible kernel functions can be used: "e" Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight. The cross-validation function involves an integral term, that is calculated using Simpson's rule.

Usage

CVbw(type_kernel = "n", vec_data, n_pts = 100, seq_bws = NULL)

Value

A list consisting of:

seq_bws

The sequence of bandwidths.

CV function

The values of the cross-validation function in the bandwidths grid.

bw

A numeric value for the cross-validation bandwidth.

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.

n_pts

The number of points used to approximate, by Simpson's rule, the integral term in the cross-validation function. Because this numeric method increases the computing time, you can check different numbers, depending on your sample size. By default, 100 points are used.

seq_bws

The sequence of bandwidths in which to compute the cross-validation function. By default, the procedure defines a sequence of 50 points, from the range of the data divided by 200 to the range divided by 2.

Author

Graciela Estévez Pérez and Alejandro Quintela del Río

References

Bowman, A.W., Hall, P. and Prvan,T. (1998), "Cross-validation for the smoothing of distribution functions", Biometrika. 85, 799-808.

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

# \donttest{
## Compute the cross-validation bandwidth for a sample of 100 random N(0,1)
## data
x <- rnorm(100, 0, 1)
num_bws <- 50
seq_bws <- seq(((max(x) - min(x))/2)/50, (max(x) - min(x))/2,length = num_bws)
hCV <- CVbw(type_kernel = "e", vec_data = x, n_pts = 200, seq_bws = seq_bws)
hCV
## The CV function is plotted
h_CV <- CVbw(vec_data = x)
h_CV$bw
plot(h_CV$seq_bws, h_CV$CVfunction, type = "l")
## Plotting the distribution function estimate controlling the grid points
## and the kernel function
ss <- quantile(x, c(0.05, 0.95))
## Number of points to be used in the representation of estimated distribution
## function
n_pts <- 100
y <- seq(ss[1], ss[2], length.out = n_pts)
F_CV <- kde(type_kernel = "e", x, y, h_CV$bw)$Estimated_values
## Plot of the theoretical and estimated distribution functions
plot(y, F_CV, type = "l", lty = 2)
lines(y, pnorm(y), type = "l", lty = 1)
legend(-1, 0.8, c("Real", "Nonparametric"), lty = 1:2)
# }