On the Goodness-of-fit Testing of Composite Hypothesis for Dynamical Systems with Small Noise

A Rabhi (1, 2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LSP-EA3263 - Laboratoire de Statistique et Processus

The problem of the goodness of-fit testing for stochastic differential equation is considered. A test statistic of the Cramér-von Mises type is proposed and its asymptotic behavior is studied. The asymptotic corresponds to the "small noise" approach, i.e., the diffusion coefficient tends to zero. The basic hypothesis is supposed to be composite parametric and the test statistics depends on the maximum likelihood estimator of the parameter. We consider two types of problems (under hypothesis): smooth (regular) and change point (singular) types. The behavior of the power function of the corresponding tests under nonparametric alternatives is discussed too.

Mots clés: Hypotheses testing; Cramér-von Mises test; diffusion process; goodness-of-fit tests

Domaines: Mathématiques [math]

A Rabhi. On the Goodness-of-fit Testing of Composite Hypothesis for Dynamical Systems with Small Noise. Annales de l'ISUP, 2009, LIII (2-3), pp.31-48. ⟨hal-03634256⟩