Bandwidth selection for the normal kernel and normal model.
Description
The bandwidth of the kernel is choose for normal model and normal kernel in such a way a contaminated point costant
times away from the mean of the distribution in scale units and mass level
has a weight no bigger than weight
.
Usage
1 2 3  wle.smooth(weight=0.31,costant=3,level=0.2,
dimension=1,raf="HD",interval=c(0.00001,0.5),
tol=10^6,max.iter=1000)

Arguments
weight 
weights associated to an observation that is 
costant 
times the contaminated point mass is away from the mean of the distribution in scale units. 
level 
mass of the contaminated point. 
dimension 
dimension of the normal distribution. 
raf 
type of Residual adjustment function to be use:

interval 
interval from which to search the root. 
tol 
the absolute accuracy to be used to achieve convergence of the algorithm. 
max.iter 
maximum number of iterations. 
Details
The wle.smooth
use uniroot
function to solve the non linear equation. No handling error is provided yet. For the Symmetric ChiSquared Disparity RAF you should use weight=0.2
and interavl=c(0.1,1)
to have a solution.
Value
wle.smooth
returns an object of class
"wle.smooth"
.
Only print method is implemented for this class.
The object returned by wle.smooth
is a list with four components: root and f.root give the location of the root and the value of the function evaluated at that
point. iter and estim.prec give the number of iterations used and an approximate estimated precision for root.
root
is the value of the bandwidth.
Author(s)
Claudio Agostinelli
References
Agostinelli, C., (1998) Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D. thesis, Department of Statistics, University of Padova.
Markatou, M., Basu, A. and Lindsay, B.G. (1998) Weighted likelihood estimating equations with a bootstrap root search. Journal of the American Statistical Association, 93, 740750.
Agostinelli, C., and Markatou, M., (2001) Test of hypotheses based on the Weighted Likelihood Methodology, Statistica Sinica, vol. 11, n. 2, 499514.
See Also
uniroot, uniroot
: one dimensional root finding.
Examples
1 2 3  library(wle)
wle.smooth()
