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Influence diagnostics for linear models with first-order autoregressive elliptical errors

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  • Paula, Gilberto A.
  • Medeiros, Marcio
  • Vilca-Labra, Filidor E.

Abstract

We introduce in this paper the class of linear models with first-order autoregressive elliptical errors. The score functions and the Fisher information matrices are derived for the parameters of interest and an iterative process is proposed for the parameter estimation. Some robustness aspects of the maximum likelihood estimates are discussed. The normal curvatures of local influence are also derived for some usual perturbation schemes whereas diagnostic graphics to assess the sensitivity of the maximum likelihood estimates are proposed. The methodology is applied to analyse the daily log excess return on the Microsoft whose empirical distributions appear to have AR(1) and heavy-tailed errors.

Suggested Citation

  • Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:339-346
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    References listed on IDEAS

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    1. Tsai, Chih-Ling & Wu, Xizhi, 1992. "Assessing local influence in linear regression models with first-order autoregressive or heteroscedastic error structure," Statistics & Probability Letters, Elsevier, vol. 14(3), pages 247-252, June.
    2. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    3. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
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    Cited by:

    1. 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.
    2. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    3. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    4. Jin-Guan Lin & Yan-Yong Zhao & Hong-Xia Wang, 2015. "Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2432-2448, November.
    5. Aline B. Tsuyuguchi & Gilberto A. Paula & Michelli Barros, 2020. "Analysis of correlated Birnbaum–Saunders data based on estimating equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 661-681, September.
    6. Clécio da Silva Ferreira & Gilberto A. Paula & Gustavo C. Lana, 2022. "Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors," Computational Statistics, Springer, vol. 37(1), pages 445-468, March.
    7. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    8. 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.
    9. Carlos Eduardo M. Relvas & Gilberto A. Paula, 2016. "Partially linear models with first-order autoregressive symmetric errors," Statistical Papers, Springer, vol. 57(3), pages 795-825, September.
    10. Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.

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