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A note on the conditional density estimate in the single functional index model
Authors:Said Attaoui
Affiliation:
  • a Département de Mathématiques, Université Djillali Liabès, BP 89, 22000, Sidi Bel Abbès, Algérie
  • b Univ. Lille Nord de France, F-59000 Lille, France
  • c ULCO, LMPA, F-62228, Calais, France
  • Abstract:In this paper, we consider the estimation of the conditional density of a scalar response variable Y, given a Hilbertian random variable X 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 tackled.
    Keywords:Conditional single-index   Conditional density   Nonparametric estimation   Semiparametric estimation   Semi-metric choice
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