roblm {roblm} | R Documentation |
MM-regression estimators
roblm(formula, data = list(), weights, na.action, model = TRUE, x = FALSE, y = FALSE, singular.ok = TRUE, contrasts = NULL, offset = NULL, control = roblm.control())
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 |
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).
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 |
Matias Salibian-Barrera
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.
data(coleman.dat, package='roblm') summary( roblm(y~., data=coleman.dat) )