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Local Influence Analysis for Penalized Gaussian Likelihood Estimators in Partially Linear Models

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  • Zhong‐Yi Zhu
  • Xuming He
  • Wing‐Kam Fung

Abstract

. Partially linear models are extensions of linear models to include a non‐parametric function of some covariate. They have been found to be useful in both cross‐sectional and longitudinal studies. This paper provides a convenient means to extend Cook's local influence analysis to the penalized Gaussian likelihood estimator that uses a smoothing spline as a solution to its non‐parametric component. Insight is also provided into the interplay of the influence or leverage measures between the linear and the non‐parametric components in the model. The diagnostics are applied to a mouthwash data set and a longitudinal hormone study with informative results.

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  • 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.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:4:p:767-780
    DOI: 10.1111/1467-9469.00363
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    Cited by:

    1. Vasconcellos, Klaus L.P. & Zea Fernandez, L.M., 2009. "Influence analysis with homogeneous linear restrictions," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3787-3794, September.
    2. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    3. Wei, Wen Hsiang, 2004. "Derivatives diagnostics and robustness for smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 335-356, June.
    4. 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.
    5. Qingming Zou & Zhongyi Zhu & Jinglong Wang, 2009. "Local influence analysis for penalized Gaussian likelihood estimation in partially linear single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 905-918, December.
    6. 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.
    7. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.

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