h_ICV {ICV}

The ICV bandwidth.

Description

Calculation of the ICV bandwidth for the Gaussian density estimator corresponding to expression (12) of Savchuk, Hart, and Sheather (2010).

Usage

h_ICV(x)

Arguments

x

numerical vector of data.

Details

Computing the ICV bandwidth for a univariate numerical data set of size n<12,058. The ICV bandwidth is consistent for the MISE optimal bandwidth (see Wand and Jones (1995)). The Gaussian kernel is used for computing the ultimate density estimate. The following values of the paramaters of the selection kernel L_ICV are used: (\alpha,\sigma)=(2.42, 5.06). The ICV bandwidth does not exceed the oversmoothed bandwidth of Terrell (1990). See expression (12) of Savchuk et al. (2010).

Value

The ICV bandwidth.

References

• Savchuk, O.Y., Hart, J.D., Sheather, S.J. (2010). Indirect cross-validation for density estimation. Journal of the American Statistical Association, 105(489), 415-423.

• Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. Chapman and Hall, London.

• Terrel, G. (1990). The maximum smoothing principle in density estimation. Journal of the American Statistical Association, 85, 470-477.

See Also

ICV, C_ICV, L_ICV, MISE_mixnorm, KDE_ICV, LocICV.

Examples

# ICV bandwidth for a random sample of size n=100 from a N(0,1) density.
h_ICV(rnorm(100))