A generalised censored least squares and smoothing spline estimators of regression function

Abstract

In this work, new regression function estimators based on the combination of two approaches are proposed. The first one is the general censorship which gathers the left, right, twice and the double censorship in the same context. The second approach is inspired from non-parametric estimation methods. The least squares and smoothing spline techniques are chosen in this paper. Moreover, the almost sure convergence of the proposed estimators to the optimal value is established. The main results extend and improve the obtained results in Boukeloua and Messaci (2016) and Kebabi et al. (2011) allowing for a more flexible methodology to deal with different censorship models including the four types of censoring (left, right, twice and double). Simulation study illustrates the performance of these estimators. We only considered a model subject to twice censorship because the other cases have already been studied in previous works.