Constants for Huber and Bisquare Psi
DESCRIPTION:
Computes tuning constants or efficiencies for Huber and bisquare psi functions. The constants can be used to obtain a location M-estimate with specified asymptotic efficiency at the Gaussian model.
USAGE: 
chb(eff=NULL, ch=<<see below>>, cb=<<see below>>)
OPTIONAL ARGUMENTS:
eff:
parameter (vector of length 1) giving the desired asymptotic efficiency of a location M-estimate at the Gaussian model. Only values between 0.7 and 1.0 are allowed. If eff is supplied, then the input values of ch and cb are ignored.
ch:
parameter giving tuning constant for Huber psi. If ch is supplied, then cb must also be supplied.
cb:
parameter giving tuning constant for bisquare psi. If cb is supplied, then ch must also be supplied.
VALUE:
if no arguments are supplied, then a 34 by 5 matrix is returned. The columns are: efficiency (1), Huber tuning constant (2), Huber beta value (3), bisquare tuning constant (4), and bisquare beta (5).

If arguments are supplied, then a list with the following components is returned:

ch:
tuning constant for the Huber psi function.
bh:
beta for the Huber psi function used to compute a Huber proposal 2 scale estimate.
eh:
estimate of the asymptotic efficiency of the location M-estimate using the Huber psi with tuning constant ch.
cb:
tuning constant for Tukey's bisquare psi function.
bb:
beta for the bisquare psi function used to compute a Huber proposal 2 scale estimate.
eb:
estimate of the asymptotic efficiency for the bisquare location estimate.
BACKGROUND:
A beta parameter is the expectation of the square of a psi function under the Gaussian distribution, and is used to achieve statistical consistency at the Gaussian model for the scale estimate in robloc.
REFERENCES:
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.

Huber, P. J. (1981). Robust Statistics. Wiley, New York.

SEE ALSO:
robloc , ar.gm .
EXAMPLES: 
chb(.95)$ch
 # tuning constant for the 95% efficient Huber M-estimate of location.


chb(ch=1.345, cb=4.685)