B-spline Estimate of the Regression Function under General Censorship Model

Abstract

In a continuity reasoning of the different estimators proposed by de Kebabi et al. [21] and recently Douas et al. [11] and Laroussi [26]. The construction of the regression function estimator is based on three axes. The first one is the application of the non-parametric estimate, namely, the least-squares technique. The second axis represents the general censorship which combines all the existing types of censorship. Hence, empirical L2-error estimates are constructed over data-dependent spaces of B-spline functions. The almost sure convergence of the proposed estimator is studied. Essentially, two models subject to twice or right censorship are assessed and this phenomena of censorship identified by the simulation shows the interest of this estimator.

Key words and phrases. Least squares regression, B-spline function, censored data, convergence, almost sure.