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

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

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

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.

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(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)))