Champion, Magali, Chastaing, Gaelle, Gadat, Sébastien and Prieur, Clémentine (2014) L2-boosting on a generalized Hoeffding decomposition for dependent variables. Application to Sensitivity Analysis. Statistica Sinica.

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Abstract

This paper is dedicated to the study of an estimator of the generalized Hoeffding decomposition. We build such an estimator using an empirical Gram-Schmidt approach and derive a consistency rate in a large dimensional setting. We then apply a greedy algorithm with these previous estimators to a sensitivity analysis. We also establish the consistency of this L2-boosting under sparsity assumptions of the signal to be analyzed. The paper concludes with numerica l experiments, that demonstrate the low computational cost of our method, as well as its efficiency on the standard benchmark of sensitivity analysis.