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Influence analysis with homogeneous linear restrictions

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  • Vasconcellos, Klaus L.P.
  • Zea Fernandez, L.M.

Abstract

We discuss the problem of influence analysis for the particular situation in which the observations must satisfy a set of homogeneous linear restrictions. We present the proof of a theoretical result showing, that for this situation, we can define a system of orthogonal influence directions, as in the unrestricted problem. As an illustration, we discuss a linear regression model where some of the explanatory variables are in the form of proportions, giving also an example with a numerical data set. Our example shows that the influence measure that is here discussed can be quite effective in identifying relevant perturbations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3787-3794
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    References listed on IDEAS

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    1. Paula, Gilberto A., 1993. "Assessing local influence in restricted regression models," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 63-79, June.
    2. Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang & Heping Zhang, 2008. "Diagnostic measures for empirical likelihood of general estimating equations," Biometrika, Biometrika Trust, vol. 95(2), pages 489-507.
    3. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    4. Menezes, Flavio M., 2008. "An Introduction to Auction Theory," OUP Catalogue, Oxford University Press, number 9780199275991.
    5. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    6. Lu, Bin & Song, Xin-Yuan, 2006. "Local influence analysis of multivariate probit latent variable models," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1783-1798, September.
    7. Frank Critchley, 2004. "Data-informed influence analysis," Biometrika, Biometrika Trust, vol. 91(1), pages 125-140, March.
    8. Hong Gu & Wing Fung, 1998. "Assessing Local Influence in Canonical Correlation Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 755-772, December.
    9. Jian-Xin Pan & Peng Bai, 2003. "Local influence analysis in the growth curve model with Rao's simple covariance structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(7), pages 771-781.
    10. Frank Critchley & Richard A. Atkinson & Guobing Lu & Elenice Biazi, 2001. "Influence analysis based on the case sensitivity function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 307-323.
    11. 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.
    12. Huang, Yufen & Kao, Tzu-Ling & Wang, Tai-Ho, 2007. "Influence functions and local influence in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3844-3861, May.
    13. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
    14. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    15. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    16. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
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