Bandwidth selection for the normal kernel and normal model.

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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

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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 scale units away from the mean of the distribution.

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:

raf="HD": Hellinger Distance RAF,

raf="NED": Negative Exponential Disparity RAF,

raf="SCHI2": Symmetric Chi-Squared Disparity RAF.

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 Chi-Squared 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, 740-750.

Agostinelli, C., and Markatou, M., (2001) Test of hypotheses based on the Weighted Likelihood Methodology, Statistica Sinica, vol. 11, n. 2, 499-514.

See Also

uniroot, uniroot: one dimensional root finding.

Examples

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