h . ST ] 3 M ay 2 01 4 Censored linear model in high dimensions

Censored data are quite common in statistics and have been studied in depth in the last years (for some early references, see Powell (1984), Muphy et al. (1999), Chay and Powell (2001)). In this paper we consider censored high-dimensional data. High-dimensional models are in some way more complex than their lowdimensional versions, therefore some different techniques are required. For the linear case appropriate estimators based on penalised regression, have been developed in the last years (see for example Bickel et al. (2009), Koltchinskii (2009)). In particular in sparse contexts the l1penalised regression (also known as LASSO) (see Tibshirani (1996), Bühlmann and van de Geer (2011) and reference therein) 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.