  Censored data are quite common in statistics and have been studied in depth
in the last years. In this paper we consider censored high-dimensional data.
  High-dimensional models are in some way more complex than their
low-dimensional versions, therefore some different techniques are required. For
the linear case appropriate estimators based on penalized regression, have been
developed in the last years. In particular in sparse contexts the
$l_1$-penalised regression (also known as LASSO) performs very well. Only few
theoretical work was done in order to analyse censored linear models in a
high-dimensional context.
  We therefore consider a high-dimensional censored linear model, where the
response variable is left-censored. We propose a new estimator, which aims to
work with high-dimensional linear censored data. Theoretical non-asymptotic
oracle inequalities are derived.
