Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics

被引：0

作者：

Bouanani O. ^{[1
]}

Laksaci A. ^{[2
]}

Rachdi M. ^{[3
]}

Rahmani S. ^{[1
]}

机构：

[1] Laboratoire de Modèles Stochastiques, Statistique et Applications, Université Docteur Moulay Taher, Saïda

[2] Department of Mathematics, College of Science, King Khalid University, Abha

[3] Université Grenoble Alpes (France), Laboratoire AGEIS, EA 7407, AGIM Team, UFR SHS, BP. 47, Grenoble Cedex 09

来源：

Behaviormetrika | 2019年 / 46卷 / 1期

关键词：

Asymptotic normality; Conditional cumulative distribution; Conditional mode; Derivatives of the conditional density; Forage quality; Functional data analysis (FDA); Local linear estimation; Small ball probability;

D O I：

10.1007/s41237-018-0057-9

中图分类号：

学科分类号：

摘要：

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. © 2018, The Behaviormetric Society.

引用

页码：199 / 233

页数：34

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