a numeric vector or matrix giving the observed
values.
yHat
a numeric vector or matrix of the same
dimensions as y giving the fitted values.
trim
a numeric value giving the trimming
proportion (the default is 0.25).
includeSE
a logical indicating whether standard
errors should be computed as well.
Details
mspe and rmspe compute the mean squared
prediction error and the root mean squared prediction
error, respectively. In addition, mape returns
the mean absolute prediction error, which is somewhat
more robust.
Robust prediction loss based on trimming is implemented
in tmspe and rtmspe. To be more precise,
tmspe computes the trimmed mean squared prediction
error and rtmspe computes the root trimmed mean
squared prediction error. A proportion of the largest
squared differences of the observed and fitted values are
thereby trimmed.
Standard errors can be requested via the includeSE
argument. Note that standard errors for tmspe are
based on a winsorized standard deviation. Furthermore,
standard errors for rmspe and rtmspe are
computed from the respective standard errors of
mspe and tmspe via the delta method.
Value
If standard errors are not requested, a numeric value
giving the prediction loss is returned.
Otherwise a list is returned, with the first component
containing the prediction loss and the second component
the corresponding standard error.
Author(s)
Andreas Alfons
References
Tukey, J.W. and McLaughlin, D.H. (1963) Less vulnerable
confidence and significance procedures for location based
on a single sample: Trimming/winsorization.
Sankhya: The Indian Journal of Statistics, Series
A, 25(3), 331–352
Oehlert, G.W. (1992) A note on the delta method.
The American Statistician, 46(1), 27–29.
See Also
cvFit, cvTuning
Examples
# fit an MM-regression model
data("coleman")
fit <- lmrob(Y~., data=coleman)
# compute the prediction loss from the fitted values
# (hence the prediction loss is underestimated in this simple
# example since all observations are used to fit the model)
mspe(coleman$Y, predict(fit))
rmspe(coleman$Y, predict(fit))
mape(coleman$Y, predict(fit))
tmspe(coleman$Y, predict(fit), trim = 0.1)
rtmspe(coleman$Y, predict(fit), trim = 0.1)
# include standard error
mspe(coleman$Y, predict(fit), includeSE = TRUE)
rmspe(coleman$Y, predict(fit), includeSE = TRUE)
mape(coleman$Y, predict(fit), includeSE = TRUE)
tmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)
rtmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)