A One-Step Weighted Likelihood Estimator for Linear model

Description

This function evaluate the One-step weighted likelihood estimator for the regression and scale parameters.

Usage

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wle.onestep(formula, data=list(), model=TRUE, x=FALSE, 
            y=FALSE, ini.param, ini.scale, raf="HD", 
            smooth=0.031, num.step=1, 
            contrasts=NULL, verbose=FALSE)

Arguments

formula

a symbolic description of the model to be fit. The details of model specification are given below.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which wle.stepwise is called from.

model, x, y

logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response.)

ini.param

starting values for the coefficients.

ini.scale

starting values for the scale parameters.

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.

num.step

number of the steps.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

verbose

if TRUE warnings are printed.

Value

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

Only print method is implemented for this class.

The object returned by wle.onestep are:

coefficients

the parameters estimator.

standard.error

an estimation of the standard error of the parameters estimator.

scale

an estimation of the error scale.

residuals

the unweighted residuals from the estimated model.

fitted.values

the fitted values from the estimated model.

tot.weights

the sum of the weights divide by the number of observations.

weights

the weights associated to each observation.

f.density

the non-parametric density estimation.

m.density

the smoothed model.

delta

the Pearson residuals.

call

the match.call().

contrasts
xlevels
terms

the model frame.

model

if model=TRUE a matrix with first column the dependent variable and the remain column the explanatory variables for the full model.

x

if x=TRUE a matrix with the explanatory variables for the full model.

y

if y=TRUE a vector with the dependent variable.

Author(s)

Claudio Agostinelli

References

Agostinelli, C., (1997) A one-step robust estimator based on the weighted likelihood methodology, Working Paper n. 1997.16, Department of Statistics, University of Padova.

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

Agostinelli, C., Markatou, M., (1998) A one-step robust estimator for regression based on the weighted likelihood reweighting scheme, Statistics \& Probability Letters, Vol. 37, n. 4, 341-350.

Agostinelli, C., (1998) Verosimiglianza pesata nel modello di regressione lineare, XXXIX Riunione scientifica della Societ\'a Italiana di Statistica, Sorrento 1998.

See Also

wle.smooth an algorithm to choose the smoothing parameter for normal distribution and normal kernel, wle.lm a function for estimating linear models with normal distribution error and normal kernel.

Examples

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#library(wle)
#library(lqs)

#data(artificial)

#result.lts <- lqs(y.artificial~x.artificial, 
#                 method = "lts")

#result.wle <- wle.onestep(y.artificial~x.artificial,
#               ini.param=result.lts$coefficients,
#               ini.scale=result.lts$scale[1])

#result.wle

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