Asymptotic properties of nonlinear estimates in stochastic models with finite design space

Luc Pronzato (1)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SYSTEMES

Under the condition that the design space is finite, new sufficient conditions for the strong consistency and asymptotic normality of the least-squares estimator in nonlinear stochastic regression models are derived. Similar conditions are obtained for the maximum-likelihood estimator in Bernoulli type experiments. Consequences on the sequential design of experiments are pointed out.

Mots clés: stochastic regressors; strong consistency; asymptotic normality; sequential design; Bernoulli trials

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Luc Pronzato. Asymptotic properties of nonlinear estimates in stochastic models with finite design space. Statistics and Probability Letters, 2009, 79, pp.2307-2313. ⟨10.1016/j.spl.2009.07.025⟩. ⟨hal-00416008⟩