Performs S-Regression using the Fast-S-Algorithm.
FastS(x, y, Scontrol=list(int = FALSE, N = 100, kk = 2, tt = 5, b= .5,
cc = 1.547, seed=NULL), beta_gamma)numeric \((n\times p)\)-matrix: Designmatrix.
numeric vector: \(n\) observations.
list of length seven: control parameters (see Details).
numeric vector: Specifies one parameter candidate of length \(p\) (see Details).
numeric vector: Fitted parameter vector.
numeric: Value of the objective function
The Fast-S-Algorithm to
efficiently perform S-Regression was published by
Salibian-Barrera and Yohai (2006). It bases on starting with a set
of N parameter candidates, locally optimizing them, but
only with kk iterations, optimizing the tt
best candidates to convergence and then choosing the best
parameter candidate. The rho-function used is the biweight
function with tuning parameter cc, the value b is
set to the expected value of the rho-function applied to the
residuals. The default cc=1.547 and b=.5 is
chosen following Rousseeuw and Yohai (1984) to obtain an
approximative breakdown point of 0.5. When setting int to TRUE,
this adds an intercept column to the design matrix. For more details see
Salibian-Barrera and Yohai (2006) or Thieler, Fried and Rathjens (2016).
The R-function FastS used in RobPer is a slightly
changed version of the R-code published in Salibian-Barrera and Yohai (2006). It was changed in order to work more efficiently,
especially when fitting step functions, and to specify one
parameter candidate in advance. For details see Thieler, Fried and Rathjens (2016).
Rousseeuw, P. J. and Yohai, V. J. (1984): Robust Regression by Means of S-estimators. In Franke, J., H<e4>rdle, W. und Martin, D. (eds.): Robust and Nonlinear Time Series Analysis. Berlin New York: Springer, Lecture Notes in Statistics No. 26, 256-272
Salibian-Barrera, M. and Yohai, V. (2006): A Fast Algorithm for S-Regression Estimates. Journal of Computational and Graphical Statistics, 15 (2), 414-427
Thieler, A. M., Fried, R. and Rathjens, J. (2016): RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression. Journal of Statistical Software, 69 (9), 1-36, <doi:10.18637/jss.v069.i09>