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Generalized local influence with applications to fish stock cohort analysis

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  • N. G. Cadigan
  • P. J. Farrell

Abstract

Summary. It is important to understand the influence of data and model assumptions on the results of a statistical analysis, and influence diagnostics are valuable tools for this. We consider local influence diagnostics for a statistical model that is fully parametric, and where estimation involves a fit function that is second order differentiable with respect to the parameters. Similarly to Cook, we study the local behaviour of influence graphs formed from perturbations to model components. However, the diagnostics that we develop are more general in that the type of model result that is used to assess influence is fairly arbitrary and must only be first order differentiable with respect to model parameters and the perturbations. This allows us to focus our influence analyses on important results, and to produce diagnostics that are meaningful to practitioners. The procedures that we propose are applied to sequential population analysis, a common method that is used to estimate the size of commercially exploited fish stocks. Our diagnostics reveal interesting patterns of influence that are not revealed by using Cook's likelihood displacement influence diagnostics. Our diagnostics lead to an increased understanding of how the data affect important estimates, and thereby provide information for assessing the potential effect of errors in model inputs. In addition, empirical comparisons illustrate that the local influence diagnostics proposed tend to provide a good description of global influence.

Suggested Citation

  • N. G. Cadigan & P. J. Farrell, 2002. "Generalized local influence with applications to fish stock cohort analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 469-483, October.
    • Handle: RePEc:bla:jorssc:v:51:y:2002:i:4:p:469-483
    DOI: 10.1111/1467-9876.00281
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    Citations

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    Cited by:

    1. 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.
    2. Miguel Angel Uribe-Opazo & Joelmir Andr� Borssoi & Manuel Galea, 2012. "Influence diagnostics in Gaussian spatial linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 615-630, July.
    3. Venezuela, Maria Kelly & Sandoval, Mônica Carneiro & Botter, Denise Aparecida, 2011. "Local influence in estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1867-1883, April.
    4. D. T. Nava & F. De Bastiani & M. A. Uribe-Opazo & O. Nicolis & M. Galea, 2017. "Local Influence for Spatially Correlated Binomial Data: An Application to the Spodoptera frugiperda Infestation in Corn," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 540-561, December.
    5. de Castro, Mario & Galea-Rojas, Manuel & Bolfarine, Heleno, 2007. "Local influence assessment in heteroscedastic measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1132-1142, October.
    6. Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    7. Xibin Zhang & Maxwell L. King, 2002. "Influence Diagnostics in GARCH Processes," Monash Econometrics and Business Statistics Working Papers 19/02, Monash University, Department of Econometrics and Business Statistics.
    8. N. G. Cadigan, 2006. "Local Influence Diagnostics for Quasi-Likelihood and Lognormal Estimates of a Biological Reference Point from Some Fish Stock and Recruitment Models," Biometrics, The International Biometric Society, vol. 62(3), pages 713-720, September.
    9. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.

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