2015/12/19 by Demián Pouzo, Demian Pouzo, Pouzo, Demian
Economics, Econometrics and Finance · Engineering · Mathematics · #Control Systems and Identification #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Fault Detection and Control Systems #Statistical Methods and Inference #Statistics Theory (math.ST) #econ.EM #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1512.06290
75 pages
openalex publication_date 2015/12/19 · arxiv created 2016/10/21 · arxiv updated 2018/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the regularized M-estimator. Our results exhibit a variance-bias trade-off, with the variance term being governed by a novel measure of the complexity of the parameter set. We also show that the mixing structure affect the variance term by scaling the number of observations; depending on the decay rate of the mixing coefficients, this scaling can even affect the asymptotic behavior. Finally, we propose a data-driven method for choosing the tuning parameters of the regularized estimator which yield the same (up to constants) concentration bound as one that optimally balances the (squared) bias and variance terms. We illustrate the results with several canonical examples.