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Influence diagnostics for the structural errors-in-variables model under the Student-t distribution

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  • Manuel Galea
  • Heleno Bolfarine
  • Filidor Vilcalabra

Abstract

The influence of observations on the parameter estimates for the simple structural errors-in-variables model with no equation error, under the Student-t distribution, is investigated using the local influence approach. The main conclusion is that the Student-t model with small degrees of freedom is able to incorporate possible outliers and influential observations in the data. The likelihood displacement approach is useful for outlier detection, especially when a masking phenomenon is present and the degrees of freedom parameter is large. The diagnostics are illustrated with two examples.

Suggested Citation

  • Manuel Galea & Heleno Bolfarine & Filidor Vilcalabra, 2002. "Influence diagnostics for the structural errors-in-variables model under the Student-t distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1191-1204.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:8:p:1191-1204
    DOI: 10.1080/0266476022000011265
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    References listed on IDEAS

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    1. Berkane, Maia & Kano, Yutaka & Bentler, Peter M., 1994. "Pseudo maximum likelihood estimation in elliptical theory: Effects of misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 18(2), pages 255-267, September.
    2. Myung Geun Kim, 2000. "Outliers and influential observations in the structural errors-in-variables model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 451-460.
    3. Fernández, C. & Steel, M.F.J., 1997. "Multivariate Student -t Regression Models : Pitfalls and Inference," Discussion Paper 1997-08, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Filidor Vilca-Labra & Reiko Aoki & Camila Zeller, 2011. "Hypotheses testing for structural calibration model," Statistical Papers, Springer, vol. 52(3), pages 553-565, August.
    2. Vidal, Ignacio & Arellano-Valle, Reinaldo B., 2010. "Bayesian inference for dependent elliptical measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2587-2597, November.
    3. Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    4. Filidor Labra & Reiko Aoki & Heleno Bolfarine, 2005. "Local influence in null intercept measurement error regression under a student_t model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 723-740.
    5. Yonghui Liu & Ruochen Sang & Shuangzhe Liu, 2017. "Diagnostic analysis for a vector autoregressive model under Student-super-′s t-distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(2), pages 86-114, May.
    6. Vidal, Ignacio & Iglesias, Pilar, 2008. "Comparison between a measurement error model and a linear model without measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 92-102, September.

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