Partial and Recombined Estimators for Nonlinear Additive Models

Nathalie Chèze (1) , Jean-Michel Poggi (2) , Bruno Portier (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Starting from a variant of an estimator using marginal integration, this paper proposes partial and recombined estimators for nonlinear additive regression models. Partial estimators are used for data analysis purposes and recombined estimators are used to improve the estimation and prediction performances for small to moderate sample sizes. In the first part of the paper, some simulations illustrate step-by-step the principle and the value of the proposed estimators, which are finally applied to the analysis and prediction of ozone concentration in Paris area. In the second part of the paper, almost sure convergence results as well as a multivariate central limit theorem and a test for partial additivity are provided.

Domaines: Statistiques [math.ST]

Nathalie Chèze, Jean-Michel Poggi, Bruno Portier. Partial and Recombined Estimators for Nonlinear Additive Models. Statistical Inference for Stochastic Processes, 2003, 6 (2), pp.155--197. ⟨10.1023/A:1023940117323⟩. ⟨hal-01633704⟩