Multivariate S-estimator (For Mastlab: Sm.m)
Reference for robust linear discriminant analysis using S-estimators:
Croux, C., and Dehon, C. (2001), "Robust linear discriminant analysis using S-estimators", The Canadian Journal of Statistics, 29, 473-492

Recently a fast procedure was developped for the S-estimator of regression by Salibian-Barrera, M. and Yohai, V.J. (Journal of Computational and graphical statistics 2006). Similarly we developed a fast algorithm to compute the S-estimation of location and covariance: for Matlab fastsloc.m and for R fastsloc.r.

Matlab program for robust linear and quadratic discriminant analysis: da.m.
As means/covariance matrices one can choose between the classical estimator, multivariate S-estimator or the (R)MCD-estimator (see Location and covariance estimation)
Matlab program to compute the influence of observations on the misclassification probability in quadratic discriminant analysis (infQDA.m).

Reference: Croux, C., and Joossens, K. (2004), "Empirical comparison of the classification performance of robust linear and quadratic discriminant analysis", Statistics for Industry and Technology, Birkhäuser Verlag Basel/Switzerland, 131-140.
Reference for influences in robust quadratic discriminant analysis:
Croux, C., and Joossens, K. (2005), "Influence of observations on the misclassification probability in quadratic discriminant analysis", Journal of Multivariate Analysis, 96 (2), 384-403.

Matlab program for Robust Linear Regression using the MM-estimator with robust standard errors: MMrse.m
Starting values of the MM-estimator is fast-S-estimator (Salibian-Barrera and Yohai, 2005), translated in Matlab by Joossens, K. fastsreg.m.

Reference: Croux, C., Dhaene, G., and Hoorelbeke, D. (2003), "Robust Standard Errors for Robust Estimators", Research Report, Dept. of Applied Economics, K.U. Leuven.

Matlab  program to compute the multivariate least trimmed squares estimator and its reweighted version. (For Matlab: mlts.m  For R: mlts.r )

Reference: Agullo,J., Croux, C., and Van Aelst, S. (2008), ``The Multivariate Least Trimmed Squares Estimator''  Journal of Multivariate Analysis,.99(3), 311-318

SPLUS  program for robust logistic regression using the Bianco and Yohai estimator and the Weigthed version of Bianco and Yohai Estimator (For SPLUS: BYlogreg.scc, WBYlogreg.scc ).

R program for robust logistic regression using the Bianco and Yohai estimator and the Weigthed version of Bianco and Yohai Estimator (BYlogreg.r.txt).

Reference: Croux, C., and Haesbroeck, G. (2003), "Implementing the Bianco and Yohai estimator for logistic regression", Computational Statistics and Data Analysis, 44, 273-295.

Example:

library(robustbase);library(rrcov)

data(vaso)

## Classical estimation

glmc <- glm(Y ~ log(Volume) + log(Rate), family=binomial, data=vaso)

print(summary(glmc))

x0 <- log(vaso[,1:2])

y <- vaso[,3]

BY <- BYlogreg(x0,y)

print(BY)

 

Robust estimation of the vector autoregressive model by a trimmed least squares procedure: (see section Robust regression)
Robust estimation of the VAR model, including robust information criteria, impulse respons functions and their standard errors. (For Matlab: robustvar.m)
Classical estimation of the VAR model, including classical information criteria, impulse respons functions and their standard errors. (For Matlab: classicvar.m)

Reference: Croux C, Joossens K (2008), "Robust estimation of the vector autoregressive model by a least trimmed squares procedure", in COMPSTAT 2008: PROCEEDINGS IN COMPUTATIONAL STATISTICS,  Ed. P. Brito, pp 489-501, Heidelberg: Phyisica Verlag 

Reference: Agullo,J., Croux, C., and Van Aelst, S. (2008), ``The Multivariate Least Trimmed Squares Estimator''  Journal of Multivariate Analysis, 99(3), 311-318.

Robust principal component analysis based on the projection-pursuit approach, in Matlab robpca.m.
In the output the following is provided:

• the "eigenvalues" using the projection-pursuit approach, using the algorithm of Croux and Ruiz-Gazen. The projection index is a scale estimator. For this one can use the Median Absolute Deviation (mad.m) or the more efficient Qn estimator of Rousseeuw and Croux, JASA 1993 (qn.m; qn.dll).

• the scores which are the projections of the data on the principal components.

The centering of the data has been done with the L1-median (for Matlab L1median.m and for R L1median.r.)

Reference: Croux, C. and Ruiz-Gazen, A. (2005), "High breakdown estimators for principal components: the Projection-pursuit approach revisited", Journal of Multivariate Analysis, 95, 206-226.

Robust estimation of the fixed effects panel data model

Reference Bramati, M. C., and Croux, C. (2007), ``Robust Estimators for the Fixed Effects Panel data Model.", Econometrics Journal, 10(3), 521-540 (pdf)

 

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