DetMM {DetR}

Robust and Deterministic Linear Regression via DetMM

Description

Function to compute the DetMM estimates of regression.

Usage

  DetMM(x,y,intercept=1,alpha=0.75,h=NULL,scale_est="scaleTau2",tuning.chi=1.54764,
tuning.psi=4.685061)

Arguments

x

Matrix of design variables. Never contains an intercept.

y

Vector of responses.

intercept

A boolean indicating whether the regression contains an intercept.

alpha

numeric parameter controlling the size of the subsets over which the determinant is minimized, i.e., alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.75. Can be a vector.

h

Integer in [ceiling((n+p+1)/2),n) which determines the number of observations which are awarded weight in the fitting process. Can be a vector. If both h and alpha are set to non default values, alpha will be ignored.

scale_est

A character string specifying the variance functional. Possible values are "Qn" or "scaleTau2".

tuning.chi

tuning constant vector for the bi-weight chi used for the ISteps.

tuning.psi

tuning constant vector for the bi-weight psi used for the MSteps.

Value

The function DetLTS returns a list with as many components as there are elements in the h. Each of the entries is a list containing the following components:

coefficients

The estimate of the coefficient vector

scale

The scale as used in the M steps.

residuals

Residuals associated with the estimator.

converged

TRUE if the IRWLS iterations have converged.

iter

number of IRWLS iterations

rweights

the “robustness weights” \psi(r_i/S) / (r_i/S).

fitted.values

Fitted values associated with the estimator.

DetS

A similar list that contains the results of (initial) returned by DetS

Author(s)

Vakili Kaveh using translation of the C code from pcaPP (by Peter Filzmoser, Heinrich Fritz, Klaudius Kalcher, see citation("pcaPP")) for the Qn and scaleTau2 (Original by Kjell Konis with substantial modifications by Martin Maechler) from robustbase (see citation("scaleTau2")). This function calls lmrob in package robustbase.

References

Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of high-dimensional datasets; Technometrics 44(4), 307–317.

Rousseeuw, P.J. and Croux, C. (1993) Alternatives to the Median Absolute Deviation; Journal of the American Statistical Association , 88(424), 1273–1283.

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

Koller, M. (2012), Nonsingular subsampling for S-estimators with categorical predictors, ArXiv e-prints, arXiv:1208.5595v1.

Koller, M. and Stahel, W.A. (2011), Sharpening Wald-type inference in robust regression for small samples, Computational Statistics & Data Analysis 55(8), 2504–2515.

Maronna, R. A., and Yohai, V. J. (2000). Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 89, 197–214.

Rousseeuw, P.J. and Yohai, V.J. (1984) Robust regression by means of S-estimators, In Robust and Nonlinear Time Series, J. Franke, W. Hardle 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, 15(2), 414–427.

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

Examples

## generate data
set.seed(1234)  # for reproducibility
n<-100
h<-c(55,76,89)
set.seed(123)
x0<-matrix(rnorm(n*2),nc=2)
y0<-rnorm(n)
out1<-DetMM(x0,y0,h=h)