DetR (version 0.0.5)

OGKCStep: Robust and Deterministic Linear Regression via OGKCStep

Description

Function to find the OGKCStep ('best') H-subset.

Usage

OGKCStep(x0, scale_est, alpha=0.5)

Arguments

x0

Matrix of continuous variables.

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 0.5.

scale_est

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

Value

best

the best subset found and used for computing the raw estimates, with length(best) == quan = h.alpha.n(alpha,n,p).

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.

Peter J. Rousseeuw (1984), Least Median of Squares Regression. Journal of the American Statistical Association 79, 871--881.

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223.

Pison, G., Van Aelst, S., and Willems, G. (2002) Small Sample Corrections for LTS and MCD. Metrika 55, 111--123.

Hubert, M., Rousseeuw, P. J. and Verdonck, T. (2012) A deterministic algorithm for robust location and scatter. Journal of Computational and Graphical Statistics 21, 618--637.

Examples

# NOT RUN {
n<-100
set.seed(123)# for reproducibility
x0<-matrix(rnorm(n*2),nc=2)
out1<-OGKCStep(x0,alpha=0.5,scale_est=pcaPP::qn)

#comparaison with DetMCD:

#a) create data

set.seed(123456)
Simulation<-DetR:::fx01()
#should be \approx 10
sqrt(min(mahalanobis(Simulation$Data[Simulation$label==0,],rep(0,ncol(Simulation$Data)),
Simulation$Sigma_u))/qchisq(0.975,df=ncol(Simulation$Data)))
a0<-eigen(Simulation$Sigma_u)
Su_ih<-(a0$vector)%*%diag(1/sqrt(a0$values))%*%t(a0$vector)
#run algorithms 
A0<-robustbase::covMcd(Simulation$Data,nsamp='deterministic',scalefn=pcaPP::qn,alpha=0.5)
A1<-OGKCStep(Simulation$Data,alpha=0.5,scale_est=pcaPP::qn)
#getbiases algorithms 
SB<-eigen(Su_ih%*%var(Simulation$Data[A1,])%*%Su_ih)$values
log10(SB[1]/SB[ncol(Simulation$Data)-1])
SB<-eigen(Su_ih%*%var(Simulation$Data[A0$best,])%*%Su_ih)$values
log10(SB[1]/SB[ncol(Simulation$Data)-1])
# }