R: Huber's Least Favourable Distribution Family Function
huber2
R Documentation
Huber's Least Favourable Distribution Family Function
Description
M-estimation of the two parameters of
Huber's least favourable distribution.
The one parameter case is also implemented.
Usage
huber1(llocation = "identitylink", k = 0.862, imethod = 1)
huber2(llocation = "identitylink", lscale = "loge",
k = 0.862, imethod = 1, zero = "scale")
Arguments
llocation, lscale
Link functions applied to the location and scale parameters.
See Links for more choices.
k
Tuning constant.
See rhuber for more information.
imethod, zero
See CommonVGAMffArguments for information.
The default value of zero means the scale parameter is
modelled as intercept-only.
Details
Huber's least favourable distribution family function is popular for
resistant/robust regression. The center of the distribution is normal
and its tails are double exponential.
By default, the mean is the first linear/additive predictor (returned
as the fitted values; this is the location parameter), and
the log of the scale parameter is the second linear/additive predictor.
The Fisher information matrix is diagonal; Fisher scoring is implemented.
The VGAM family function huber1() estimates only the
location parameter. It assumes a scale parameter of unit value.
Value
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Note
Warning: actually, huber2() may be erroneous since the
first derivative is not continuous when there are two parameters
to estimate. huber1() is fine in this respect.
The response should be univariate.
Author(s)
T. W. Yee.
Help was given by Arash Ardalan.
References
Huber, P. J. and Ronchetti, E. (2009)
Robust Statistics, 2nd ed. New York: Wiley.