wle.normal: Robust Estimation in the Normal Model
In wle: Weighted Likelihood Estimation

Description Usage Arguments Value Author(s) References See Also Examples

wle.normal is used to robust estimate the location and the scale parameters via Weighted Likelihood, when the sample is iid from a normal distribution with unknown mean and variance.

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wle.normal(x, boot=30, group, num.sol=1, raf="HD",
           smooth=0.003, tol=10^(-6), equal=10^(-3), 
           max.iter=500, verbose=FALSE)

`x`	a vector contain the observations.
`boot`	the number of starting points based on boostrap subsamples to use in the search of the roots.
`group`	the dimension of the bootstap subsamples. The default value is max(round(size/4),2) where size is the number of observations.
`num.sol`	maximum number of roots to be searched.
`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.
`smooth`	the value of the smoothing parameter.
`tol`	the absolute accuracy to be used to achieve convergence of the algorithm.
`equal`	the absolute value for which two roots are considered the same. (This parameter must be greater than `tol`).
`max.iter`	maximum number of iterations.
`verbose`	if `TRUE` warnings are printed.

wle.normal returns an object of class "wle.normal".

Only print method is implemented for this class.

The object returned by wle.normal are:

`location`	the estimator of the location parameter, one value for each root found.
`scale`	the estimator of the scale parameter, one value for each root found.
`residuals`	the residuals associated to each observation, one column vector for each root found.
`tot.weights`	the sum of the weights divide by the number of observations, one value for each root found.
`weights`	the weights associated to each observation, one column vector for each root found.
`f.density`	the non-parametric density estimation.
`m.density`	the smoothed model.
`delta`	the Pearson residuals.
`freq`	the number of starting points converging to the roots.
`call`	the match.call().
`tot.sol`	the number of solutions found.
`not.conv`	the number of starting points that does not converge after the `max.iter` iteration are reached.

Claudio Agostinelli

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., (1998) Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D Thesis, Department of Statistics, University of Padova.

wle.smooth an algorithm to choose the smoothing parameter for normal distribution and normal kernel.

library(wle)

data(cavendish)

result <- wle.normal(cavendish)

result

result <- wle.normal(cavendish,boot=20,num.sol=1)

barplot(result$weights,col=2,xlab="Observations",
        ylab="Weights",ylim=c(0,1),
        names.arg=seq(1:length(result$weights)))