lambda00 {enetLTS}  R Documentation 
family="binomial"
Use bivariate winsorization to estimate the smallest value of the upper limit for the penalty parameter.
lambda00(x,y,normalize=TRUE,intercept=TRUE,const=2,prob=0.95,
tol=.Machine$double.eps^0.5,eps=.Machine$double.eps,...)
x 
a numeric matrix containing the predictor variables. 
y 
a numeric vector containing the response variable. 
normalize 
a logical indicating whether the winsorized predictor
variables should be normalized or not (the
default is 
intercept 
a logical indicating whether a constant term should be
included in the model (the default is 
const 
numeric; tuning constant to be used in univariate winsorization (the default is 2). 
prob 
numeric; probability for the quantile of the

tol 
a small positive numeric value used to determine singularity issues in the computation of correlation estimates for bivariate winsorization. 
eps 
a small positive numeric value used to determine whether the robust scale estimate of a variable is too small (an effective zero). 
... 
additional arguments if needed. 
The estimation procedure is done with similar approach as in Alfons et al. (2013). But the Pearson correlation between y and the jth predictor variable xj on winsorized data is replaced to a robustified pointbiserial correlation for logistic regression.
A robust estimate of the smallest value of the penalty parameter for
enetLTS regression (for family="binomial"
).
For linear regression, we take exactly same procedure as in Alfons et al., which is based on the Pearson correlation between y and the jth predictor variable xj on winsorized data. See Alfons et al. (2013).
Fatma Sevinc KURNAZ, Irene HOFFMANN, Peter FILZMOSER
Maintainer: Fatma Sevinc KURNAZ <fatmasevinckurnaz@gmail.com>;<fskurnaz@yildiz.edu.tr>
Kurnaz, F.S., Hoffmann, I. and Filzmoser, P. (2017) Robust and sparse estimation methods for high dimensional linear and logistic regression. Chemometrics and Intelligent Laboratory Systems.
Alfons, A., Croux, C. and Gelper, S. (2013) Sparse least trimmed squares regression for analyzing highdimensional large data sets. The Annals of Applied Statistics, 7(1), 226–248.
set.seed(86)
n < 100; p < 25 # number of observations and variables
beta < rep(0,p); beta[1:6] < 1 # 10% nonzero coefficients
sigma < 0.5 # controls signaltonoise ratio
x < matrix(rnorm(n*p, sigma),nrow=n)
e < rnorm(n,0,1) # error terms
eps <0.05 # %10 contamination to only class 0
m < ceiling(eps*n)
y < sample(0:1,n,replace=TRUE)
xout < x
xout[y==0,][1:m,] < xout[1:m,] + 10; # class 0
yout < y # wrong classification for vertical outliers
# compute smallest value of the upper limit for the penalty parameter
l00 < lambda00(xout,yout)