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We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James--Stein type estimators for Gaussian processes by Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401--424].
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares si
In this paper, we address the estimation of the sensitivity indices called Shapley eects. These sensitivity indices enable to handle dependent input variables. The Shapley eects are generally dicult to estimate, but they are easily computable in the
In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter $theta$. We suppose that the process is discretely observed at the instants (t n i)i=0,...,n with $Delta$n = sup i=0,...,n--1 (t
This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. (2018) considering the local stationary version o
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.