Nonparametric estimation of level sets under minimal assumptions

Baillo et al. [Baillo, A., Cuesta-Albertos, J.A., Cuevas, A., 2001. Convergence rates in nonparametric estimation of level sets. Statist. Probab. Lett. 53, 27–35] established L1L1-convergence results for nonparametric estimators of level sets, for i.i.d. sequences, under a highly technical assumption imposed on the underlying density function. In this article we establish the same results (with the same rates of convergence) without imposing such technical conditions. Furthermore, the i.i.d. assumption used in the cited paper will be relaxed to the one based on αα-mixing sequences. We require no additional conditions to establish our results.