roblm {roblm}R Documentation

MM-regression estimators

Description

MM-regression estimators

Usage

roblm(formula, data = list(), weights, na.action, 
        model = TRUE, x = FALSE, y = FALSE, singular.ok = TRUE, 
        contrasts = NULL, offset = NULL, control = roblm.control())

Arguments

formula formula
data data
weights weights
na.action na.action
model model
x x
y y
singular.ok singular.ok
contrasts contrasts
offset offset
control control

Details

This function computes and MM-regression estimator as described in Yohai (1987). It uses a bi-square re-desceding score function, and by default it returns a highly robust and highly efficient estimator (with 50% breakdown point and 95% asymptotic efficiency for normal errors). It uses an S-estimator (Rousseeuw and Yohai, 1984) for the errors which is also computed with a bi-square score function. The S-estimator is computed using the Fast-S algorithm of Salibian-Barrera and Yohai (2006). Standard errors are computed using the formulas for homoscedastic and independent errors of Croux, Dhaene and Hoorelbeke (2003).

Value

An object of class roblm. A list that includes the following components:

coef The MM-regression estimator
scale The S-scale estimator
s The auxiliary S-regression estimator
cov The estimated covariance matrix of the regression coefficients
residuals Residuals associated with the MM-estimator
fitted.values Fitted values associated with the MM-estimator
converged TRUE if the IRWLS iterations converged

Note

Author(s)

Matias Salibian-Barrera

References

Croux, C., Dhaene, G. and Hoorelbeke, D. (2003) Robust standard errors for robust estimators, Discussion Papers Series 03.16, K.U. Leuven, CES.

Rousseeuw, P.J. and Yohai, V.J. (1984) Robust regression by means of S-estimators, In Robust and Nonlinear Time Series, J. Franke, W. H"ardle and R. D. Martin (eds.). Lectures Notes in Statistics 26, 256-272, Springer Verlag, New York.

Salibian-Barrera, M. and Yohai, V.J. (2006) A fast algorithm for S-regression estimates, Journal of Computational and Graphical Statistics, in press.

Yohai, V.J. (1987) High breakdown-point and high efficiency estimates for regression, The Annals of Statistics 15, 642-65.

See Also

roblm.control

Examples

data(coleman.dat, package='roblm')
summary( roblm(y~., data=coleman.dat) )

[Package roblm version 0.6 Index]