# lambda00

##### Upper limit of the penalty parameter for `family="binomial"`

Use bivariate winsorization to estimate the smallest value of the upper limit for the penalty parameter.

- Keywords
- robust

##### Usage

```
lambda00(x,y,normalize=TRUE,intercept=TRUE,const=2,prob=0.95,
tol=.Machine$double.eps^0.5,eps=.Machine$double.eps,...)
```

##### Arguments

- 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

`TRUE`

).- intercept
a logical indicating whether a constant term should be included in the model (the default is

`TRUE`

).- const
numeric; tuning constant to be used in univariate winsorization (the default is 2).

- prob
numeric; probability for the quantile of the \(\chi^{2}\) distribution to be used in bivariate winsorization (the default is 0.95).

- 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.

##### Details

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 point-biserial correlation for logistic regression.

##### Value

A robust estimate of the smallest value of the penalty parameter for
enetLTS regression (for `family="binomial"`

).

##### Note

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).

##### References

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 high-dimensional large data sets. *The Annals of Applied Statistics*, 7(1), 226--248.

##### See Also

##### Examples

```
# NOT RUN {
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 signal-to-noise 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)
# }
```

*Documentation reproduced from package enetLTS, version 0.1.0, License: GPL (>= 3)*