We propose a minimax statistical framework adapted to nonparametric estimation in deterministic dynamical system, which highlights the importance of the recurrence property of the observed process. Estimators are evaluated on the basis of a weighted uniform norm. The weight function rn depends...

We deal with the issue of testing the specification of a regression function. As a leading case, we consider testing for a pure noise model. We study the smallest local alternatives that can be detected asymptotically in a minimax sense. We propose a simple testing procedure that has asymptotic...

The authors propose a nonparametric test for white noise hypothesis in a regression model. The test is based on a regressogram estimate, which bin width is selected using a penalty method similar to the AIC, BIC, and C'ps MAllows criteria.