The finite sample properties of sparse M-estimators with pseudo-observations

We provide finite sample properties of general regularized statistical criteria in the presence pseudo-observations. Under restricted strong convexity assumption unpenalized loss function and regularity conditions on penalty, we derive non-asymptotic error bounds M-estimator. This penalized framework with pseudo-observations is then applied to M-estimation some usual copula-based models. These theoretical results are supported by an empirical study.