R: Class of "Psi Functions" for M-Estimation

psi_func-class {robustbase} | R Documentation

## Class of "Psi Functions" for M-Estimation

### Description

The class `"psi_func"` is used to store psi functions for M-estimation. In particular, an object of the class contains rho(x), its derivative psi(x), the weight function ψ(x)/x, and first derivative of ψ, `Dpsi =` ψ'(x).

### Objects from the Class

Objects can be created by calls of the form `new("psi_func", ...)`, but preferably by `psiFunc(...)`.

### Slots

`rho`:

  the rho() function, an object of class `"functionX"`. This is used to formulate the objective function; ρ() can be regarded as generalized negative log-likelihood.

`psi`:

  psi() is the derivative of ρ, psi(x) = d/dx rho(x); also of class `"functionX"`.

`wgt`:

  The weight function ψ(x)/x, of class `"functionX"`.

`Dpsi`:

  the derivative of ψ, Dpsi(x) = psi'(x); of class `"functionX"`.

`Dwgt`:

  the derivative of the weight function, of class `"functionX"`, is generated automatically if `psiFunc` constructor is used.

`tDefs`:

  named numeric vector of tuning parameter Default values.

`Erho`:

  A function of class `"functionXal"` for computing E[ρ(X)] when X is standard normal N(0,1).

`Epsi2`:

  A function of class `"functionXal"` for computing E[ψ^2(X)] when X is standard normal.

`EDpsi`:

  A function of class `"functionXal"` for computing E[ψ'(X)] when X is standard normal.

`name`:

  Name of psi-function used for printing.

`xtras`:

  Potentially further information.

### Methods

Currently, only `chgDefaults()`, `plot()` and `show()`.

### Author(s)

Martin Maechler

### See Also

`psiFunc`.

### Examples

    str(huberPsi, give.attr = FALSE)

    plot(hampelPsi)# calling the plot method (nicely showing "all" !)

[Package robustbase version 0.95-0 Index]