Robust Estimation in the Poisson Model

Description

wle.poisson is used to robust estimate the lambda parameters in the poisson model via Weighted Likelihood.

Usage

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wle.poisson(x, boot=30, group, num.sol=1,
   raf=c("HD", "NED", "GKL", "PWD", "SCHI2"),
   tau=NULL, tol=10^(-6), equal=10^(-3), 
   max.iter=500, verbose=FALSE)

Arguments

x

a vector contain the number of success.

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(length(x)/4),2).

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="GKL": Generalized Kullback-Leibler RAF family with parameter tau.

raf="PWD": Power Divergence Measure RAF family with parameter tau.

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

tau

this is to set the member inside the GKL and PWD family. It must be in [0,1] for GKL and in [-1, Inf] for PWD.

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

Only print method is implemented for this class.

The object returned by wle.poisson are:

lambda

the estimator of the lambda parameter, one value 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.

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.

Author(s)

Claudio Agostinelli

References

Markatou, M., Basu, A., and Lindsay, B.G., (1997) Weighted likelihood estimating equations: The discrete case with applications to logistic regression, Journal of Statistical Planning and Inference, 57, 215-232.

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

Examples

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library(wle)

set.seed(1234)

x <- rpois(40,5)
wle.poisson(x)

x <- c(rpois(40,5),rpois(10,20))
wle.poisson(x)

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