Johanna Kappus (Institut für Mathematik, Humboldt-Universität zu Berlin)

Nonparametric estimation of linear functionals of a Lévy measure

vendredi 28 mai 2010, 9h30 - 10h45

Salle de réunion, espace Turing

A Lévy process X of pure jump type having finite variation on compacts is
observed at discrete, equidistant time points. Let nu denote the corresponding jump measure. We are interested in the problem of estimating a linear
functional from the finite measure x nu(dx).

We propose an estimator which is based on Fourier methods. The rates of
convergence depend on the smoothness of the test function f as well as on
the decay of the characteristic functions of X1 and of x nu(dx), which are both
unknown. This raises the need for a data driven estimator which adapts automatically to the unknown smoothness.

There is a strong resemblance of our problem to the problem of estimating
a linear functional in the convolution model. We investigate this connection
to see to what extent the techniques which have been developed so far for
adaptive estimation in the convolution model are applicable in our setting.