wle.binomial: Robust Estimation in the Binomial Model
In wle: Weighted Likelihood Estimation

Description Usage Arguments Value Author(s) References Examples

wle.binomial is used to robust estimate the proportion parameters via Weighted Likelihood.

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

`x`	a vector contain the number of success in each `size` trials.
`size`	number of trials.
`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="SCHI2"`: Symmetric Chi-Squared Disparity RAF.
`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.binomial returns an object of class "wle.binomial".

Only print method is implemented for this class.

The object returned by wle.binomial are:

`p`	the estimator of the proportion 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.

Claudio Agostinelli

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.

library(wle)

set.seed(1234)

x <- rbinom(20,p=0.2,size=10)
wle.binomial(x,size=10)

x <- c(rbinom(20,p=0.2,size=10),rbinom(10,p=0.9,size=10))
wle.binomial(x,size=10)