Influence measures in nonparametric regression model with symmetric random errors

Germán Ibacache-Pulgar (), Cristian Villegas (), Javier Linkolk López-Gonzales () and Magaly Moraga ()
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Germán Ibacache-Pulgar: Faculty of Sciences, Institute of Statistics, University of Valparaíso
Cristian Villegas: Department of Exact Sciences, University of São Paulo
Javier Linkolk López-Gonzales: Facultad de Ingeniería y Arquitectura, Universidad Peruana Unión
Magaly Moraga: Instituto de Estadística, Universidad Austral de Chile

Statistical Methods & Applications, 2023, vol. 32, issue 1, No 1, 25 pages

Abstract: 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.

Keywords: Nonparametric regression models; Local influence; Peña measured; Cook’s distance; Cubic spline (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10260-022-00648-z

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