In a recent paper Lee and Na (2001) introduced a test for a parametric form of the distribution of the innovations in autoregressive models, which is based on the integrated squared error of the nonparametric density estimate from the residuals and a smoothed version of the parametric fit of the density. They derived the asymptotic distribution under the null-hypothesis, which is the same as fo...

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Major (1979), Taqqu (1979)). This process is non-Gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the Brownian motion on a finite interval and...

This work aims to compare the performance of new methods to estimate the Soil Moisture Content (SMC) of bare soils from their spectral signatures in the reflective domain (0.4-2.5 µm) in comparison with widely used spectral indices like Normalized Soil Moisture Index (NSMI) and Water Index SOIL (WISOIL). Indeed, these reference spectral indices use wavelengths located in the water vapour absorp...

Let Z be the Rosenblatt process with the representation Z t = ∫ t

The paper concerns the image, level and sojourn time sets associated with sample paths of Rosenblatt process. We obtain results regarding Hausdorff (both classical macroscopic), packing intermediate dimensions, logarithmic pixel densities. As a preliminary step we also establish inversion property process, as well some technical points distribution Z.

Location-scale invariant Bickel-Rosenblatt goodness-of-fit tests (IBR tests) are considered in this paper to test the hypothesis that f , the common density function of the observed independent d-dimensional random vectors, belongs to a null location-scale family of density functions. The asymptotic behaviour of the test procedures for fixed and non-fixed bandwidths is studied by using an unify...