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Influence measures in nonparametric regression model with symmetric random errors
Author(s)
Ibacache‐Pulgar, Germán
University of Valparaíso
Villegas, Cristian
Universidade de São Paulo
Moraga, Magaly
Austral University of Chile
Date Issued
25 de junio de 2022
Type
Article
Volume
32
Issue
1
Series/Report No.
Statistical Methods & Applications
Start Page
1
End Page
25
ISSN
1613-981X
1618-2510
Abstract
In this paper we present several diagnostic measures for the class of nonparametric regression models with symmetric random errors, which includes all continuous and symmetric distributions. In particular, we derive some diagnostic measures of global influence such as residuals, leverage values, Cook’s distance and the influence measure proposed by Peña (Technometrics 47(1):1–12, 2005) to measure the influence of an observation when it is influenced by the rest of the observations. A simulation study to evaluate the effectiveness of the diagnostic measures is presented. In addition, we develop the local influence measure to assess the sensitivity of the maximum penalized likelihood estimator of smooth function. Finally, an example with real data is given for illustration.