Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics
Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics
复制标题
高维统计中一些条件非参数函数参数的渐近正态性
DOI：
10.1007/s41237-018-0057-9
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Saâdia Rahmani
中科院分区：
文献类型：
--
作者：
Oussama Bouanani;Ali Laksaci;Mustapha Rachdi;Saâdia Rahmani
本文讨论了函数数据分析框架中某些条件参数的估计量分布的收敛性。事实上，我们考虑的模型的输入是函数类型，输出是标量。然后，我们建立（1）条件分布函数和（2）条件密度的逐次导数的非参数局部线性估计量的渐近正态性。此外，作为副产品，我们推导出条件模式的局部线性估计量的渐近正态性。最后，为了显示我们的结果的兴趣，从实际的角度来看，我们进行了一项计算研究，首先是模拟数据，然后是有关饲料质量的一些真实数据。
This paper deals with the convergence in distribution of estimators of some conditional parameters in the Functional Data Analysis framework. In fact, we consider models where the input is of functional kind and the output is a scalar. Then, we establish the asymptotic normality of the nonparametric local linear estimators of (1) the conditional distribution function and (2) the successive derivatives of the conditional density. Moreover, as by-product, we deduce the asymptotic normality of the local linear estimator of the conditional mode. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning the forage quality.