Abstract: In the random censorship from the right model,we consider the asymptotics of Bahadur-Kiefer process based on smoothed PL and its quantile processes. We prove that with the different choice of smoothing parameter the asymptotic distribution on smoothed Bahadur-Kiefer process can be completely different. We obtain a complete characterization of the possible limits.

Key words: Random censorship, Kernel-smoothing, Bahadur-Kiefer process, Asymptotic distribution