A note on the conditional density estimate in single functional index model

Said Attaoui (1) , Ali Laksaci (1) , Elias Ould Said (2)

1 Département de Mathématiques
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

In this paper, we consider estimation of the conditional density of a scalar response variable given a Hilbertian random variable when the observations are linked with a single-index structure. We establish the pointwise and the uniform almost complete convergence (with the rate) of the kernel estimate of this model. As an application, we show how our result can be applied in the prediction problem via the conditional mode estimate. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is also discussed but not attacked.

Mots clés: Conditional single-index; Conditional density; Nonparametric estimation; Semiparametric estimation; Semi-metric choice

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Said Attaoui, Ali Laksaci, Elias Ould Said. A note on the conditional density estimate in single functional index model. Statistics and Probability Letters, 2011, 81 (1), pp.45-53. ⟨10.1016/j.spl.2010.09.017⟩. ⟨hal-00698847⟩