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Local influence diagnostics with forward search in regression analysis

Author

Listed:
  • Reiko Aoki

    (Universidade de São Paulo)

  • Juan P. M. Bustamante

    (Universidade de São Paulo)

  • Gilberto A. Paula

    (Universidade de São Paulo)

Abstract

Regression analysis is one of the most widely used statistical techniques. It is well known that the least squares estimates is sensitive to atypical and/or influential observations. Many methodologies were proposed to detect influential observations considering case deletion (global influence). On the other hand, Cook (J R Stat Soc Ser B 48(2):133–169, 1986) developed a general and powerful methodology to obtain a group of observations that might be jointly influential considering the local influence. However, these techniques may fail to detect masked influential observations. In this paper, we propose a methodology to detect masked influential observations in a local influence framework considering the forward search (Atkinson and Riani, Robust diagnostic regression analysis, Springer, New York, 2000). The usefulness of the proposed methodology is illustrated with data sets which were previously analyzed in the literature to detect outliers and/or influential observations. Masked influential observations were successfully identified in these studies. The proposed methodology may be used in any model where the local influence analysis (Cook 1986) is appropriate.

Suggested Citation

  • Reiko Aoki & Juan P. M. Bustamante & Gilberto A. Paula, 2022. "Local influence diagnostics with forward search in regression analysis," Statistical Papers, Springer, vol. 63(5), pages 1477-1497, October.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-021-01279-4
    DOI: 10.1007/s00362-021-01279-4
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    References listed on IDEAS

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    1. Anthony C. Atkinson & Marco Riani & Andrea Cerioli, 2018. "Cluster detection and clustering with random start forward searches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 777-798, April.
    2. Andrea Cerioli & Alessio Farcomeni & Marco Riani, 2019. "Wild adaptive trimming for robust estimation and cluster analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(1), pages 235-256, March.
    3. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    4. Pedro Galeano & Daniel Peña, 2019. "Rejoinder on: Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 363-368, June.
    5. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "The power of monitoring: how to make the most of a contaminated multivariate sample," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 559-587, December.
    6. Pedro Galeano & Daniel Peña, 2019. "Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 289-329, June.
    7. Paula, Gilberto A., 1993. "Assessing local influence in restricted regression models," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 63-79, June.
    8. Fukang Zhu & Shuangzhe Liu & Lei Shi, 2016. "Local influence analysis for Poisson autoregression with an application to stock transaction data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 4-25, February.
    9. Aurea Grané & Giancarlo Manzi & Silvia Salini, 2021. "Smart Visualization of Mixed Data," Stats, MDPI, vol. 4(2), pages 1-14, June.
    10. 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.
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