DESCRIPTION:

USAGE:

smooth.splineRob(x, y, lambda = "RCp", lambda.range = c(0, 1), chuber =
1.345)

REQUIRED ARGUMENTS:

x
a numeric vector containing the values of the predictor variable.
y
response variable, of the same length as x.

OPTIONAL ARGUMENTS:

lambda
the smoothing parameter corresponding to the formulation of the reference paper. Note that it is not the same parameter as spar in the function smooth.spline() in S-PLUS. In fact spar = (lambda * sigma)/epsiprime/(max(xx) - min(xx))^3. If lambda = "cv" then an optimal lambda is chosen using crossvalidation. If lambda = "RCp" then an optimal lambda is chosen using the RCp criterion. The default is "RCp".
lambda.range
interval in which the optimal smoothing parameter has to be found when lambda = "cv" or lambda = "RCp".
chuber
tuning constant of the Huber psi function. The default value is set to 1.345.

VALUE:

a list with class "smooth.splineRob" containing the following components:
estim
the fitted M-type smoothing spline corresponding to the ordered xx.
sigmahat
the associated estimation of scale (Huber Proposal 2).
sigma.ext
the external estimation of scale used in the construction of RCp (if Smat = T).
x
the ordered distinct values of xx.
yin
the y-values used at the unique x values (weighted averages of the input yy).
myo
value of match(xx, unique(sort(xx))). This allows one to recover the vector of fitted values with respect to the original xx by considering estim[myo].
weights
weights used in the fit. This has the same length as xx, and in the case of ties, will consist of the accumulated weights at each unique value of x.
Smatrix
the smoother matrix S, if Smat=T.
diagS
the diagonal elements of the smoother matrix S.
epsiprime
the expectation of the derivative of the psi function.
epsicarre
the expectation of the squared psi function.
cv.score
the value of the robust cross-validation criterion.
RCp
the value of the robust Cp criterion, if Smat=T.
chuber
the tuning constant used for the fit.
lambda
the smoothing parameter used for the fit.
call
an image of the call that created the object with all arguments named.

REFERENCES:

Eva Cantoni and Elvezio Ronchetti, "Resistant Selection of the Smoothing Paramater for Smooting Splines", 2000, Statistics and Computing, to appear.
http://www.unige.ch/ses/metri/cantoni/txt/ECER2001report.ps.

SEE ALSO:

.

EXAMPLES:

attach(ethanol)
plot(E, NOx)
temp.cv <- smooth.splineRob(E, NOx, lambda = "cv")
lines(temp.cv)