Resumen de Censored linear model in high dimensions
Patric Müller, Sara van de Geer
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 l1-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
