A Nonparametric Estimator for the Kolmogorov Canonical Measure via the Empirical Characteristic Function

• Activity Number: 685
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guillermo Basulto-Elias*+ and Miguel Nakamura-Savoy and Víctor Manuel Pérez-Abreu
• Companies: Iowa State University and Center for Research in Mathematics and Center for Research in Mathematics
• Keywords: Nonparametric ; Kolmogorov canonical measure ; Characteristic function ; Minimize ; Sieves ; Levy process

Abstract

Levy processes (e.g., Brownian motion, compound Poisson processes, stable Levy processes) can be represented through a trend parameter and Kolmogorov canonical measure, which appear in the characteristic function. We propose a nonparametric estimator of this measure for a Levy process with finite second moment. A sieves-type approximation to the Kolmogorov canonical measure is considered, which depends on parameters that represent jumps. The estimator is the result of minimizing the distance between the empirical characteristic function and the characteristic function based on the parameters of the sieves-type approximation of the Kolmogorov canonical measure; both characteristic functions are evaluated at several points. Some representative examples are shown to illustrate the performance of this estimator.