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

查看全文 作　　者：Fadila [1]Benaissa;Abdelmalek [2]Gagui;Abdelhak [2]Chouaf 机构地区：[1]University Oran 1 Ahmed Ben Bella Oran,Oran,Algeria;[2]Laboratory of Statistics and Stochastic Processes,Djillali Liabes University,Sidi Bel Abbes,Algeria 出　　处：《Statistical Theory and Related Fields》索引2022年第6卷第3期,共12页 摘　　要：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,and 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,wecomplete 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. 关 键 词：Mean squared error single functional index conditional density function nonparametric estimation local linear estimation asymptotic normality functional data