Eftychia Solea Σεμινάριο
ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ ΙΟΥΝΙΟΣ 2021
Eftychia Solea, CREST, ENSAI, Rennes, France
Nonparametric and high-dimensional functional graphical models
ΠΕΜΠΤΗ 24/6/2021, 12:30
We consider the problem of constructing nonparametric undirected graphical models for high- dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish concentration inequalities for the resulting estimators allowing both the number of predictors and the number of functional principal components to diverge to infinity with increasing sample size. We also investigate the empirical performance of our method through simulation studies and a real data application.