Statistical Methods & Applications

, Volume 25, Issue 2, pp 227–249 | Cite as

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions

  • Shuangzhe Liu
  • Víctor Leiva
  • Tiefeng Ma
  • Alan Welsh


The local influence method has proven to be a useful and powerful tool for detecting influential observations on the estimation of model parameters. This method has been widely applied in different studies related to econometric and statistical modelling. We propose a methodology based on the Lagrange multiplier method with a linear penalty function to assess local influence in the possibly heteroskedastic linear regression model with exact restrictions. The restricted maximum likelihood estimators and information matrices are presented for the postulated model. Several perturbation schemes for the local influence method are investigated to identify potentially influential observations. Three real-world examples are included to illustrate and validate our methodology.


Information matrix Local influence Restricted least-squares estimator Restricted maximum likelihood estimator 

Mathematics Subject Classification

62J05 62J20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Shuangzhe Liu
    • 1
  • Víctor Leiva
    • 2
    • 3
  • Tiefeng Ma
    • 4
  • Alan Welsh
    • 5
  1. 1.Faculty of Education, Science, Technology and MathematicsUniversity of CanberraCanberraAustralia
  2. 2.Faculty of Engineering and SciencesAdolfo Ibáñez UniversityViña del MarChile
  3. 3.Institute of StatisticsUniversity of ValparaísoValparaísoChile
  4. 4.School of StatisticsSouthwestern University of Finance and EconomicsChengduChina
  5. 5.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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