Scalar or vector of
length 4 which specifies the value of the tuning
constant c (scalar greater than 0 which controls the
robustness/efficiency of the estimator)
and the prefixed values of paramters a, b, c
ctuning(1) = tuning constant which will multiply
parameters a, b and c of Hampel rho (psi) function
ctuning(2) = paramter a of Hampel rho (psi) function
ctuning(3) = paramter b of Hampel rho (psi) function
ctuning(4) = paramter c of Hampel rho (psi) function
Remark: if length(ctuning)==1 values of a, b and c will be
set to a=2*ctuning b=4*ctuning c=4*ctuning
With these choices, if ctuning=1 the
resulting influence function is nearly identical to the
biweight with parameter 8.
Function HApsider transforms vector as follows
HApsi(u) = \left\{
\begin{array}{cc}
1 & |u| <= a \\
0 & a <= |u| < b \\
-\frac{a}{c-b} & b <= |u| < c \\
0 & |u| >= c
\end{array} \right.
where a= ctuning(2) *ctuning(1).
b= ctuning(3) *ctuning(1).
c= ctuning(4) *ctuning(1).
The default (if input ctuning is a scalar) is
a= 2*ctuning.
b= 4*ctuning.
c= 8*ctuning.
It is necessary to have 0 <= a <= b <= c
References
Hoaglin, D.C., Mosteller, F., Tukey, J.W. (1982), "Understanding Robust and
Exploratory Data Analysis", Wiley, New York.