bandwidth.parameter {dad}

Parameter of the normal reference rule

Description

Computation of the parameter of the normal reference rule in order to estimate the (matrix) bandwidth.

Usage

bandwidth.parameter(p, n)

Arguments

p

sample dimension.

n

sample size.

Details

The parameter is equal to:

h = (\frac{4}{n(p+2)})^{\frac{1}{p+4}}

It is based on the minimisation of the asymptotic mean integrated square error in density estimation when using the Gaussian kernel method (Wand and Jones, 1995).

Value

Returns the value required by the functions fpcad, fmdsd, fdiscd.misclass and fdiscd.predict when their argument windowh is set to NULL.

Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard

References

Boumaza, R., Yousfi, S., Demotes-Mainard, S. (2015). Interpreting the principal component analysis of multivariate density functions. Communications in Statistics - Theory and Methods, 44 (16), 3321-3339.

Wand, M. P., Jones, M. C. (1995). Kernel Smoothing. Boca Raton, FL: Chapman and Hall.

Examples

    # Sample size :
    n <- 20
    # Number of variables :
    p <- 3
    bandwidth.parameter(p, n)