Efficient estimation for nonparametric regression with small intensity noise

Jeudi, 28 octobre 2021 - 10:15 - 11:15
We develop an efficient nonparametric estimation theory for continuous time regression models with non-Gaussian Lévy noises in the case when the unknown functions belong to Sobolev ellipses. Using the Pinsker’s approach, we provide a sharp lower bound for the normalized asymptotic mean square accuracy. We find constructive sufficient conditions for the ellipse coefficients under which we develop efficient estimation methods. We show that the obtained conditions hold for the ellipse coefficients of an exponential form.

Spectral estimation of Hawkes processes from count data

Spectral estimation of Hawkes processes from count data

Jeudi, 14 octobre 2021 - 10:15 - 11:15

Hawkes processes are a family of stochastic processes for which the occurrence of any event increases the probability of further events occurring. When count data are only observed in discrete time, we propose a spectral approach for the estimation of Hawkes processes, by means of Whittle's estimation method. To get asymptotic properties for the estimator, we prove alpha-mixing properties for the series of counts, using the Galton-Watson properties of the cluster representation of Hawkes processes.