J_admissible: Admissible Rank Transformations of Eichner & Stute (2013)

In kader: Kernel Adaptive Density Estimation and Regression

Description

This is just a wrapper for the functions J1, J2, and u -> √ 3 * (2u - 1) which implement the admissible transformations for the three cases for c. For mathematical details see eq. (15.16) and (15.17) in Eichner (2017) and/or Eichner & Stute (2013).

Usage

J_admissible(u, cc = sqrt(5))

Arguments

u	Numeric vector.
cc	Numeric constant, defaults to √ 5.

Details

Basically, for cc in [√(5/3), √ 5]:

J_admissible(u, cc) = J1(u, cc) if cc < √ 3,

J_admissible(u, cc) = J2(u, cc) if cc > √ 3, and

J_admissible(u, cc) = sqrt(3) * (2*u - 1) if cc = √ 3.

Value

Vector of same length and mode as u.

Note

The admissible rank transformations require c to be in [√(5/3), √ 5]. If cc does not satisfy this requirement a warning (only) is issued. The default cc = sqrt(5), i.e., c = √ 5, yields the optimal rank transformation.

See Also

J1 and J2.

Examples

par(mfrow = c(1, 2), mar = c(3, 3, 0.5, 0.5), mgp = c(1.7, 0.7, 0))
example(J1)
example(J2)

kader documentation built on May 1, 2019, 10:13 p.m.