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Influence measures in nonparametric regression model with symmetric random errors

Author

Listed:
  • Germán Ibacache-Pulgar

    (Faculty of Sciences, Institute of Statistics, University of Valparaíso
    Interdisciplinary Center for Atmospheric and Astro-Statistical Studies, Universidad de 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)

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.

Suggested Citation

  • Germán Ibacache-Pulgar & Cristian Villegas & Javier Linkolk López-Gonzales & Magaly Moraga, 2023. "Influence measures in nonparametric regression model with symmetric random errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 1-25, March.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00648-z
    DOI: 10.1007/s10260-022-00648-z
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    References listed on IDEAS

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    4. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    5. Zhong‐Yi Zhu & Xuming He & Wing‐Kam Fung, 2003. "Local Influence Analysis for Penalized Gaussian Likelihood Estimators in Partially Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 767-780, December.
    6. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    7. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    8. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
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