Influence measures in nonparametric regression model with symmetric random errors

Germán Ibacache-Pulgar, Cristian Villegas, Javier Linkolk López-Gonzales, Magaly Moraga

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalStatistical Methods and Applications
Volume32
Issue number1
DOIs
StatePublished - Mar 2023

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