JSM 2005 Online Program

Abstract #303397

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Activity Number:	229
Type:	Contributed
Date/Time:	Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Section on Nonparametric Statistics
Abstract - #303397
Title:	Nonparametric Estimation of Levy Densities Based on Continuous and Discrete Data
Author(s):	Jose E. Figueroa-Lopez*+ and Christian Houdre
Companies:	Purdue University and Georgia Institute of Technology
Address:	2550 Yeager Rd 116, W Lafayette, IN, 47906, United States
Keywords:	Levy processes ; model selection ; penalized projection estimators ; adaptive estimation
Abstract:	In this paper, nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the ``jumps'' of X and discrete-data-based approximations are introduced. A model selection approach made up of two steps is investigated. The first step consists of selecting 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 variance Gamma processes---models of key importance in risky asset price modeling driven by Levy processes---is presented.

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