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Local influence analysis for penalized Gaussian likelihood estimation in partially linear single-index models

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Abstract

Single-index model is a potentially tool for multivariate nonparametric regression, generalizes both the generalized linear models(GLM) and the missing-link function problem in GLM. In this paper, we extend Cook’s local influence analysis to the penalized Gaussian likelihood estimator based on P-spline for the partially linear single-index model. Some influence measures, based on the minor perturbation of the model, are derived for the penalized least squares estimation. An illustrative example is also presented.

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Authors and Affiliations

  1. Department of Statistics, East China Normal University, Shanghai, 200062, People’s Republic of China

    Qingming Zou & Jinglong Wang

  2. College of Economics and Management, Nanhua University, Hengyang, 421001, People’s Republic of China

    Qingming Zou

  3. Department of Statistics, Fudan University, Shanghai, 200433, People’s Republic of China

    Zhongyi Zhu

Authors
  1. Qingming Zou
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  2. Zhongyi Zhu
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  3. Jinglong Wang
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Corresponding author

Correspondence to Zhongyi Zhu.

Additional information

This work was supported by Natural Science Foundation of China Grants 10671038.

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Zou, Q., Zhu, Z. & Wang, J. Local influence analysis for penalized Gaussian likelihood estimation in partially linear single-index models. Ann Inst Stat Math 61, 905–918 (2009). https://doi.org/10.1007/s10463-007-0158-9

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  • DOI: https://doi.org/10.1007/s10463-007-0158-9

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