# Robust and Deterministic Linear Regression via OGKCStep Function to find the OGKCStep ('best') H-subset. ```r 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. ## Returns - **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 ```r 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]) ``` ## Author(s) Large part of the the code are from function `.detmcd` in package robustbase , , see citation("robustbase")

OGKCStep function