Function to compute the DetMM estimates of regression.
DetMM(x,y,intercept=1,alpha=0.75,h=NULL,scale_est="scaleTau2",tuning.chi=1.54764,
tuning.psi=4.685061)Matrix of design variables. Never contains an intercept.
Vector of responses.
A boolean indicating whether the regression contains an intercept.
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.
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.
A character string specifying the variance functional. Possible values are "Qn" or "scaleTau2".
tuning constant vector for the bi-weight chi used for the ISteps.
tuning constant vector for the bi-weight psi used for the MSteps.
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:
The estimate of the coefficient vector
The scale as used in the M steps.
Residuals associated with the estimator.
TRUE if the IRWLS iterations have converged.
number of IRWLS iterations
the “robustness weights” \(\psi(r_i/S) / (r_i/S)\).
Fitted values associated with the estimator.
A similar list that contains the results of (initial) returned by DetS
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.
# NOT RUN {
## 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)
# }
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