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Data-informed influence analysis

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  • Frank Critchley

Abstract

The likelihood-based influence analysis methodology introduced in Cook (1986) uses a parameterised space of local perturbations of a base model. It is frequently the case that such perturbation schemes involve more parameters of interest and perturbation parameters than there are observations, and hence the perturbation space is often explored rather than estimated, where exploration means discovering the effect on inference of putatively choosing values of perturbation parameters. This paper considers the question of what can be learned about the perturbation parameters through the data. It extends Cook's methodology to take account of information available in the data regarding the perturbations, the general philosophy of the approach being that of learn what you can and explore what you cannot learn. Both local and global analyses are possible, as indicated by the data, while the eigenvector sign indeterminacy of local analysis is removed. Numerical examples are given and further developments are briefly indicated. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Frank Critchley, 2004. "Data-informed influence analysis," Biometrika, Biometrika Trust, vol. 91(1), pages 125-140, March.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:1:p:125-140
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    Cited by:

    1. Marc G. Genton & Peter Hall, 2016. "A tilting approach to ranking influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 77-97, January.
    2. Ferrari, Davide & Zheng, Chao, 2016. "Reliable inference for complex models by discriminative composite likelihood estimation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 68-80.
    3. Cristian Roner & Claudia Di Caterina & Davide Ferrari, 2021. "Exponential Tilting for Zero-inflated Interval Regression with Applications to Cyber Security Survey Data," BEMPS - Bozen Economics & Management Paper Series BEMPS85, Faculty of Economics and Management at the Free University of Bozen.
    4. K. Anaya-Izquierdo & P. Marriott, 2007. "Local mixtures of the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(1), pages 111-134, March.
    5. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    6. 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.
    7. Peter Hall & D. M. Titterington & Jing‐Hao Xue, 2009. "Tilting methods for assessing the influence of components in a classifier," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 783-803, September.

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