huber2 {VGAM} | 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 = "loglink",
k = 0.862, imethod = 1, zero = "scale")
Arguments
llocation , lscale |
Link functions applied to the location and scale parameters.
See |
k |
Tuning constant.
See |
imethod , zero |
See |
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.
See Also
rhuber
,
uninormal
,
laplace
,
CommonVGAMffArguments
.
Examples
set.seed(1231); NN <- 30; coef1 <- 1; coef2 <- 10
hdata <- data.frame(x2 = sort(runif(NN)))
hdata <- transform(hdata, y = rhuber(NN, mu = coef1 + coef2 * x2))
hdata$x2[1] <- 0.0 # Add an outlier
hdata$y[1] <- 10
fit.huber2 <- vglm(y ~ x2, huber2(imethod = 3), hdata, trace = TRUE)
fit.huber1 <- vglm(y ~ x2, huber1(imethod = 3), hdata, trace = TRUE)
coef(fit.huber2, matrix = TRUE)
summary(fit.huber2)
## Not run: # Plot the results
plot(y ~ x2, data = hdata, col = "blue", las = 1)
lines(fitted(fit.huber2) ~ x2, data = hdata, col = "darkgreen", lwd = 2)
fit.lm <- lm(y ~ x2, hdata) # Compare to a LM:
lines(fitted(fit.lm) ~ x2, data = hdata, col = "lavender", lwd = 3)
# Compare to truth:
lines(coef1 + coef2 * x2 ~ x2, data = hdata, col = "orange",
lwd = 2, lty = "dashed")
legend("bottomright", legend = c("truth", "huber", "lm"),
col = c("orange", "darkgreen", "lavender"),
lty = c("dashed", "solid", "solid"), lwd = c(2, 2, 3))
## End(Not run)