# 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

 `1` ```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

 ```1 2 3``` ```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.