psi_func-class function

Class of "Psi Functions" for M-Estimation

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 $\psi(x)/x$, and first derivative of $\psi$, Dpsi = $\psi'(x)$. class

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 $\rho$, $psi(x) = d/dx rho(x)$; 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 t uning parameter Def ault values.
• Erho:: A function of class "functionXal" for computing $E[\rho(X)]$ when $X$ is standard normal $N(0,1)$.
• 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(s)

Martin Maechler

See Also

psiFunc.

Examples

str(huberPsi, give.attr = FALSE)

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