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 references, see Powell (J Econom 25(3):303–325, 1984 ), Murphy et al. (Math Methods Stat 8(3):407–425, 1999 ), Chay and Powell (J Econ Perspect 15(4):29–42, 2001 )]. 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 penalised regression have been developed in the last years [see for example Bickel et al. (Ann Stat 37(4):1705–1732, 2009 ), Koltchinskii (Bernoulli 15:799–828, 2009 )]. In particular, in sparse contexts, the $$l_1$$ l 1 -penalised regression (also known as LASSO) [see Tibshirani (J R Stat Soc Ser B 58:267–288, 1996 ), Bühlmann and van de Geer (Statistics for high-dimensional data. Springer, Heidelberg, 2011 ) and reference therein] performs very well. Only few theoretical work was done 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. Copyright Sociedad de Estadística e Investigación Operativa 2016