2015/11/18 by Johanna Kappus, Kappus, Johanna
Mathematics · #62G05 #62G07 #62G20 #62M05 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G05 #msc:62G07 #msc:62G20 #msc:62M05 #stat.TH
paper · pdf · doi:10.48550/arxiv.1511.05780
24 pages, 4 tables
arxiv created 2015/11/20 · arxiv updated 2015/11/23
We consider nonparametric statistical inference for Lévy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk bounds are derived and the corresponding rates of convergence are discussed under global as well as local regularity assumptions. Moreover, minimax optimality is proved for the estimator of the jump measure. Some numerical examples are given to illustrate the practical performance of the estimation procedure.