wle.normal.multi: Robust Estimation in the Normal Multivariate Model

In wle: Weighted Likelihood Estimation

Description

wle.normal.multi is used to robust estimate the location and the covariance matrix via Weighted Likelihood, when the sample is iid from a normal multivariate distribution with unknown means and variance matrix.

Usage

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

Arguments

x	a matrix 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),(var*(var+1)/2+var)) where size is the number of observations and var is the number of variables.
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.

Value

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

Only print method is implemented for this class.

The object returned by wle.normal.multi are:

location	the estimator of the location parameters, one vector for each root found.
variance	the estimator of the covariance matrix, one matrix 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.
tot.sol	the number of solutions found.
call	the match.call().
not.conv	the number of starting points that does not converge after the max.iter iteration are reached.

Author(s)

Claudio Agostinelli

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.

See Also

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

Examples

library(wle)

data(iris)

smooth <- wle.smooth(dimension=4,costant=4,
                    weight=0.5,interval=c(0.3,0.7))

x.data <- as.matrix(iris[iris[,5]=="virginica",1:4])

result <- wle.normal.multi(x.data,boot=20,group=21,
                           num.sol=3,smooth=smooth$root)

result

result <- wle.normal.multi(x.data,boot=20,group=21,
                           num.sol=1,smooth=smooth$root)

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

wle documentation built on May 29, 2017, 11:48 a.m.