**1. Introduction**

Let {(*Xi*, *Zi*, *<sup>δ</sup>i*)}*<sup>n</sup> <sup>i</sup>*=<sup>1</sup> be a simple random sample of (*X*, *Z*, *δ*) with *X* being the covariate, *Z* = min{*T*, *C*} the observed variable and *δ* = *IT*≤*<sup>C</sup>* the uncensoring indicator. Usually, *T* is the time until the occurrence of an event and *C* is the censoring time. The generalised product-limit estimator of the conditional survival function proposed in [1] is given by

$$\hat{S}\_h^{\mathbb{B}}(t|\mathbf{x}) = \prod\_{i=1}^n \left( 1 - \frac{I\_{\{Z\_i \le t, \delta i = 1\}} w\_{n,i}(\mathbf{x})}{1 - \sum\_{j=1}^n I\_{\{Z\_j < Z\_i\}} w\_{n,j}(\mathbf{x})} \right) \tag{1}$$

where

$$w\_{n,i}(\mathbf{x}) = \frac{K\left((\mathbf{x} - \mathbf{X}\_i)/h\right)}{\sum\_{j=1}^{n} K\left((\mathbf{x} - \mathbf{X}\_j)/h\right)}$$

with *i* = 1, ..., *n* and *h* = *hn* is the bandwidth for the covariable. This estimator depends on a smoothing parameter which is, in practice, unknown. Therefore, finding a method for automatic selection of this bandwidth is truly interesting and very helpful in the analysis of real data subject to censoring. Bootstrap confidence intervals of *S*(*t*|*x*) are also proposed.
