Statistical testing of the covariance matrix rank in multidimensional neuronal models
Séminaire Probabilités & Statistique
11/04/2019 - 14:00 Mme Anna Melnykova (UGA) Salle 106 - Batiment IMAG
The aim of this work is to develop a testing procedure which determines the rank of the noise in a multidimensional stochastic process from discrete observations of this process on a fixed time interval [0, T] sampled with a time step ∆. We use the random perturbation approach, used for non-random matrix rank estimation, to a stochastic diffusion process. We conduct a simulation study on multidimensional stochastic models of neuronal activity: FitzHugh-Nagumo model and a stochastic approximation of the Hawkes process. Our primary goal is to control the perturbation rate, which ensures a non-degenerate statistics used in the test, and study its influence on the test accuracy for a fixed step size ∆. Keywords. Statistical tests, hypoelliptic diffusions, neuronal FitzHugh-Nagumo model, computational statistics.