6 papers
Equivariance, Curvature and Symmetry in Functional Covariance Estimation
Jocelyn Nembe
Statistical procedures for functional data are routinely applied after changes of time scale, registration, or other reparametrisations, although it is generally unclear when the r…
How far can symmetry help? Phase transitions and symmetry selection in sparse functional data analysis
Jocelyn Nembe
In sparse functional data analysis, where curves are each observed at random points, the covariance surface undergoes a sharp phase transition: if the covariance has smooth…
Spectral Equivariance and Geometric Transport in Reproducing Kernel Hilbert Spaces: A Unified Framework for Orthogonal Polynomial and Kernel Estimation
Jocelyn Nembé
We develop a unified geometric framework for nonparametric estimation based on the notion of Twin Kernel Spaces, defined as orbits of a reproducing kernel under a group action. Thi…
Concentration of Measure under Diffeomorphism Groups: A Universal Framework with Optimal Coordinate Selection
Jocelyn Nembé
We establish a universal framework for concentration inequalities based on invariance under diffeomorphism groups. Given a probability measure on a space and a diffeomorphi…
TwinKernel Estimation for Point Process Intensity Functions: Adaptive Nonparametric Methods via Orbital Regularity
Jocelyn Nembé
We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale…
Adaptive Nonparametric Estimation via Kernel Transport on Group Orbits: Oracle Inequalities and Minimax Rates
Jocelyn Nembe
We develop a unified framework for nonparametric functional estimation based on kernel transport along orbits of discrete group actions, which we term \emph{Twin Spaces}. Given a b…