FastS: S-Regression using the Fast-S-Algorithm

In RobPer: Robust Periodogram and Periodicity Detection Methods

S-Regression using the Fast-S-Algorithm

Description

Performs S-Regression using the Fast-S-Algorithm.

Usage

FastS(x, y, Scontrol=list(int = FALSE, N = 100, kk = 2, tt = 5, b= .5,
 cc = 1.547, seed=NULL), beta_gamma)

Arguments

x	numeric (n,p)-matrix: Designmatrix.
y	numeric vector: n observations.
Scontrol	list of length seven: control parameters (see Details).
beta_gamma	numeric vector: Specifies one parameter candidate of length p (see Details).

Details

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).

Value

beta	numeric vector: Fitted parameter vector.
scale	numeric: Value of the objective function

Author(s)

Matias Salibian-Barrera and Victor Yohai, modified by Anita M. Thieler

References

Rousseeuw, P. J. and Yohai, V. J. (1984): Robust Regression by Means of S-estimators. In Franke, J., Härdle, 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>

See Also

Applied in RobPer. See FastTau for example.

RobPer documentation built on June 13, 2022, 1:06 a.m.