wle.normal: Robust Estimation in the Normal Model

Description

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.

Usage

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

Arguments

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.

Value

wle.normal returns an object of class "wle.normal".
Only print method is implemented for this class.
The object returned by wle.normal are:
locationthe estimator of the location parameter, one value for each root found.
scalethe estimator of the scale parameter, one value for each root found.
residualsthe residuals associated to each observation, one column vector for each root found.
tot.weightsthe sum of the weights divide by the number of observations, one value for each root found.
weightsthe weights associated to each observation, one column vector for each root found.
freqthe number of starting points converging to the roots.
callthe match.call().
tot.solthe number of solutions found.
not.convthe number of starting points that does not converge after the max.iter iteration are reached.

References

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.

Examples

Run this code

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)))