Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations

In this paper, we discuss the global L-2 error of the nonlinear wavelet estimators of the density function in the Besov space B-pq(s), when the survival times form a stationary alpha-mixing sequence, and prove that the nonlinear wavelet estimators can achieve the optimal rate of convergence, which is similar to the result of Donoho et al. (1996). Also, the optimal convergence rates of the nonlinear wavelet estimators of the hazard rate function in the Besov space B-pq(s) are considered, which had not been discussed by Donoho et al. (1996) for complete data in the i.i.d. case.