Mathematics – Statistics Theory
Scientific paper
2004-12-17
Mathematics
Statistics Theory
68 pages, 19 figures, submitted to Annals of Statistics
Scientific paper
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the ``best'' rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.
Figueroa-Lopez Enrique
Houdré Christian
No associations
LandOfFree
Nonparametric estimation for Levy processes with a view towards mathematical finance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonparametric estimation for Levy processes with a view towards mathematical finance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonparametric estimation for Levy processes with a view towards mathematical finance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-159604