Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data

被引:2
作者
Bouzebda, Salim [1 ]
Souddi, Youssouf [2 ]
Madani, Fethi [2 ]
机构
[1] Univ Technol Compiegne, Lab Math Appl Compiegne LMAC, F-60200 Compiegne, France
[2] Univ Saida Dr Moulay Tahar, Lab Stochast Models Stat & Applicat, POB 138 EN NASR, Saida 20000, Algeria
基金
英国科研创新办公室;
关键词
conditional distribution; small ball probability; missing at random; empirical process; ergodic functional data; semi-metric space; covering number; CENTRAL LIMIT-THEOREMS; PARTIALLY LINEAR-MODELS; NONPARAMETRIC REGRESSION; RESPONSES; UNIFORM; ERROR; EFFICIENCY;
D O I
10.3390/math12030448
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper's findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator's asymptotic (1-alpha)-confidence interval is provided for 0<alpha<1 as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology.
引用
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页数:22
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