Multiplicative deconvolution in survival analysis under dependency

We study the non-parametric estimation of an unknown survival function S with support on R+ based a sample multiplicative measurement errors. The proposed fully-data driven procedure is Mellin transform and regularisation inverse by spectral cut-off. upcoming bias-variance trade-off dealt data-driven choice cut-off parameter. In order to discuss bias term, we consider Mellin-Sobolev spaces which characterize regularity through decay its transform. For analysis variance i.i.d. case incorporate dependent observations in form Bernoulli shift processes beta mixing sequences. Additionally, show minimax-optimality over estimator.