help sregress-------------------------------------------------------------------------------

Title

sregress-- S-robust regression

Syntax

sregressdepvar[indepvars] [if] [in] [,option]

optionsDescription -------------------------------------------------------------------------

noconstantsuppress constant termoutliergenerate outlyingness measuresgraphgenerate the outlier identification graphical toolreplicset the number of sub-sampling to consider

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Description

sregressfits an S-estimator of regression ofdepvaronvarlist. An S-estimator of regression is a robust fitting approach which minimizes a (rho) function of the regression residuals which is even, non decreasing for positive values and less increasing than the square function. The function used here is a Tukey Biweight leading to a Guassian efficiency of 28.7%

Options+-------+ ----+ Model +------------------------------------------------------------

noconstant; see[R] estimation options.

+-----------+ ----+ Algorithm +--------------------------------------------------------

graph; Displays a graphic where outliers are flagged according to their type.

outlier; Four outlyingness measures are calculated. The first (S_stdres) contains the robust standardized residuals, the second (S_outlier) flags outliers in the vertical dimension (i.e. observations associated with robust standardized residual larger than 2.25), the third (Robust_distance) contains robust distances and the fourth (MCD_outlier) flags outliers in the horizontal dimension (i.e. observations associated with robust distances larger than the 97.5th percentile of a Chi-quared).

replic; The number of subsets associated to the underlying algorithm is set by default using the formula replic=log(1-0.99)/log(1-(1-0.2)^(p+1)) wherepis the number of explanatory variables. This can be changed using the replic option.

Saved results

sregresssaves the following ine():Scalars

e(scale)robust residual scalee(N)number of observationse(df_m)model degrees of freedome(df_r)residual degrees of freedomMacros

e(cmd)sregresse(properties)b VMatrices

e(b)coefficient vectore(V)variance-covariance matrix of the estimatorsFunctions

e(sample)marks estimation sample

ExamplesSetup

. webuse autoRobust regression

. xi: sregress price mpg headroom trunk weight length turndisplacement gear_ratio i.rep78 foreignSame as above, but asking for outlyingness measures

. xi: sregress price mpg headroom trunk weight length turndisplacement gear_ratio i.rep78 foreign, outliers

References

Dehon, C., Gassner, M. and Verardi, V. (2008), "Beware of "Good" Outliers and Overoptimistic Conclusions", forthcoming in the Oxford Bulletin of Economics and Statistics

Rousseeuw, P. J. and Yohai, V. (1987), "Robust Regression by Means of S-estimators", in Robust and Nonlinear Time Series Analysis, edited by J. Franke, W. Härdle and D. Martin, Lecture Notes in Statistics No. 26, Springer Verlag, Berlin, pp. 256-272.

Rousseeuw, P. J. and van Zomeren, B. (1990), "Unmasking Multivariate Outliers and Leverage Points", Journal of the American Statistical Association, 85, pp. 633-639.

Salibian-Barrera, M. and Yohai, V. (2006). "A fast algorithm for S-regression estimates". Journal of Computational and Graphical Statistics, 15, 414-427.

Also seeOnline:

[R] qreg,[R] regress;[R] rreg, mmregress, mregress, msregress, mcd