Large deviations for M-estimators

Abstract: We consider parametric models, not necessarily i.i.d, whose distribu-tions depend on a parameter θ ∈ Θ ⊂ Rd. The parameter space Θ is a compact and convex subset of Rd. We give a large deviations principle for a M-estimator of θ. Then we apply our result to some statistical models such as elliptic models, nonlinear models and generalized linear models. Key words: M-estimator, large deviations principle, elliptic models, nonlinear models, generalized linear models.