In this PhD Thesis we investigate the geometry of random fields on compact Riemannian
manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic …

We study the asymptotic behaviour of needlets-based approximate maximum likelihood
estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We …

In the random coefficients binary choice model, a binary variable equals 1 iff an index X^⊤β
is positive. The vectors X and β are independent and belong to the sphere S^d-1 in R^d. We …

We study the weak convergence (in the high-frequency limit) of the parameter estimators of
power spectrum coefficients associated with Gaussian, spherical and isotropic random …

This work is concerned with the study of the adaptivity properties of nonparametric
regression estimators over the d-dimensional sphere within the global thresholding …

The aim of this paper is to establish rates of convergence to Gaussianity for wavelet
coefficients on circular Poisson random fields. This result is established by using the Stein …

The aim of this paper is to study nonparametric regression estimators on the sphere based
on needlet block thresholding. The block thresholding procedure proposed here follows the …

This paper is concerned with the estimation of the partial derivatives of a probability density
function of directional data on the d-dimensional torus within the local thresholding …

This work develops the asymptotic properties (weak consistency and Gaussianity), in the
high-frequency limit, of approximate maximum likelihood estimators for the spectral …

In this work, we study the L p-risk with p≥ 1 of nonparametric density estimators by using
wavelet method in the framework of circular data. In particular, these estimators are based …