We provide a systematic convergence analysis of the Hessian operator estimator from
random samples supported on a low dimensional manifold. We show that the impact of the …

We study Hessian estimators for functions defined over an-dimensional complete analytic
Riemannian manifold. We introduce new stochastic zeroth-order Hessian estimators using …

This paper studies the fitting of Hessian or its inverse with stochastic Hessian-vector
products. A Hessian fitting criterion, which can be used to derive most of the commonly used …

We study stochastic zeroth-order gradient and Hessian estimators for real-valued functions
in. We show that, via taking finite difference along random orthogonal directions, the …

The well known Weyl's asymptotic formula gives an approximation to the number N ω of
eigenvalues (counted with multiplicities) on an interval [0, ω] of the Laplace-Beltrami …

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M
of dimension d embedded in R^ D given a noisy sample from the manifold. We assume that …

We propose nonparametric estimators for the second-order central moments of possibly
anisotropic spherical random fields, within a functional data analysis context. We consider a …

The well known Weyl's asymptotic formula gives an approximation to the number N _ ω of
eigenvalues (counted with multiplicities) on an interval 0,\, ω of an elliptic second-order …

By methods of stochastic analysis on Riemannian manifolds, we develop two approaches to
determine an explicit constant $ c (D) $ for an $ n $-dimensional compact manifold $ D …

The family of Mat\'ern kernels are often used in spatial statistics, function approximation and
Gaussian process methods in machine learning. One reason for their popularity is the …