Class of "Psi Functions" for M-Estimation

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

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; \(\rho()\) can be regarded as generalized negative log-likelihood.

psi:

\(\psi()\) is the derivative of \(\rho\), \(\psi(x) = \frac{d}{dx} \rho(x)\); also of class "functionX".

wgt:

The weight function \(\psi(x)/x\), of class "functionX".

Dpsi:

the derivative of \(\psi\), \(Dpsi(x) = psi'(x)\); 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.

%%% FIXME : Replace these by *methods*

Erho:

A function of class "functionXal" for computing \(E[\rho(X)]\) when \(X\) is standard normal \(\mathcal{N}(0,1)\).

Epsi2:

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

EDpsi:

A function of class "functionXal" for computing \(E[\psi'(X)]\) 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

Martin Maechler

See also

psiFunc.

Examples

str(huberPsi, give.attr = FALSE)
#> Formal class 'psi_func' [package "robustbase"] with 11 slots
#>   ..@ rho  :Formal class 'functionX' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (x, k = 1.345)  
#>   ..@ psi  :Formal class 'functionX' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (x, k = 1.345)  
#>   ..@ wgt  :Formal class 'functionX' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (x, k = 1.345)  
#>   ..@ Dpsi :Formal class 'functionX' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (x, k = 1.345)  
#>   ..@ Dwgt :Formal class 'functionX' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (x, k = 1.345)  
#>   ..@ tDefs: Named num 1.34
#>   ..@ Erho :Formal class 'functionXal1' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (k = 1.345)  
#>   ..@ Epsi2:Formal class 'functionXal1' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (k = 1.345)  
#>   ..@ EDpsi:Formal class 'functionXal1' [package "robustbase"] with 1 slot
#>   .. .. ..@ .Data:function (k = 1.345)  
#>   ..@ name : chr "Huber"
#>   ..@ xtras:List of 1
#>   .. ..$ tuningP:List of 1
#>   .. .. ..$ k: num 1.34

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