Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

ISSN 2475-4269

CN 31-2182/O1

Abdelmalek Gagui ,

Laboratory of Statistics and Stochastic Processes, Djillali Liabes University, Sidi Bel Abbes, Algeria

Abdelhak Chouaf

Laboratory of Statistics and Stochastic Processes, Djillali Liabes University, Sidi Bel Abbes, Algeria

Pages | Received 22 Nov. 2020, Accepted 05 Jul. 2021, Published online: 02 Sep. 2021,

Abstract
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This paper deals with the conditional density estimator of a real response variable given a

functional random variable (i.e., takes values in an infinite-dimensional space). Specifically, we focus on the functional index model, this approach represents a good compromise between nonparametric and parametric models. Then we give under general conditions and when the variables are independent, the quadratic error and asymptotic normality of estimator by local linear method, based on the single-index structure. Finally, we complete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

References

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