Optimal classification of Gaussian functional data with noise
We study a functional classification problem in which the goal is to determine whether an observed function arises from a Gaussian model or from the same model contaminated with noise. We derive the optimal (Bayes) rule and present several useful formulations for relevant scenarios. We also allow the noise‑generating process to have a nonzero mean function, which extends existing results for homoscedastic Gaussian functional data with non‑stochastic trends and enables the derivation of new rules for detecting stochastic trends. Finally, we propose an estimator of the optimal rule based on training samples and evaluate its performance using both simulated and real data.
Palabras clave: Supervised classification functional data stochastic trend Gaussian process