Given n equidistant realisations of a Lévy process (Lt; t = 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit...

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an...

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local...

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the...

Stochastic delay differential equations (SDDEs for short) appear naturally in the description of many processes, e.g. in population dynamics with a time lag due to an age-dependent birth rate (Scheutzow 1981), in economics where a certain "time to build" is needed (Kydland and Prescott 1982) or...

In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error...

Given n equidistant realisations of a Lévy process (Lt; t = 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit...