Influence diagnostics and model validation for the generalized extreme-value nonlinear regression model

References

• Fisher RA, Tippett LHC. Limiting forms of the frequency distribution of the largest or smallest member of a sample. Math Proc Camb Philos Soc. 1928;24(2):180–190. doi: 10.1017/S0305004100015681
   Google Scholar
• Gnedenko B. Sur la distribution limite du terme maximum d'une serie aleatoire. Ann Math. 1943;44(3):423–453. doi: 10.2307/1968974
   Google Scholar
• Gumbel EJ. Statistics of extremes. New York: Columbia University Press; 1958.
   Google Scholar
• Barreto-Souza W, Vasconcellos KLP. Bias and skewness in a general extreme-value regression model. Comput Stat Data Anal. 2011;55(3):1379–1393. doi: 10.1016/j.csda.2010.09.028
   Web of Science ®Google Scholar
• Cordeiro GM, Udo MCT. Bias correction in generalized nonlinear models with dispersion covariates. Commun Stat Theory Methods. 2008;37(14):2219–2225. doi: 10.1080/03610920801931895
   Web of Science ®Google Scholar
• Ferrari SLP, Pinheiro EC. Small-sample likelihood inference in extreme-value regression models. J Stat Comput Simul. 2014;84(3):582–595. doi: 10.1080/00949655.2012.720686
   Web of Science ®Google Scholar
• Ferrari SLP, Pinheiro EC. Small-sample one-sided testing in extreme value regression models. AStA Adv Stat Anal. 2016;100(1):79–97. doi: 10.1007/s10182-015-0251-y
   Web of Science ®Google Scholar
• Ferrari SLP, Cribari-Neto F. Beta regression for modelling rates and proportions. J Appl Stat. 2004;31(7):799–815. doi: 10.1080/0266476042000214501
   Web of Science ®Google Scholar
• Atkinson AC. Plots, transformations and regression: an introduction to graphical methods of diagnostic regression analysis. New York: Oxford University Press; 1985. (Oxford Statistical Science Series; Vol. 1).
   Google Scholar
• Wei BC, Hu YQ, Fung WK. Generalized leverage and its applications. Scandinavian J Stat. 1998;24:25–37. doi: 10.1111/1467-9469.00086
   Google Scholar
• Cook RD, Weisberg S. Residuals and influence in regression. New York: Chapman & Hall; 1982.
   Google Scholar
• Xie FC, Wei BC. Diagnostics analysis for log-Birnbaum-Saunders regression models. Comput Stat Data Anal. 2007;51(9):4692–4706. doi: 10.1016/j.csda.2006.08.030
   Web of Science ®Google Scholar
• Pregibon D. Logistic regression diagnostics. Ann Stat. 1981;9(4):705–724. doi: 10.1214/aos/1176345513
   Web of Science ®Google Scholar
• Cook DR. Assessment of local influence. J R Stat Soc B. 1986;48(2):133–169.
   Google Scholar
• Cook DR. Detection of influential observations in linear regression. Technometrics. 1977;19(1):15–18.
   Web of Science ®Google Scholar
• Cook DR. Influential observations in linear regression. J Am Stat Assoc. 1979;74(365):169–174. doi: 10.1080/01621459.1979.10481634
   Web of Science ®Google Scholar
• Schwarzmann B. A connection between local-influence analysis and residual diagnostics. Technometrics. 1991;33(1):103–104. doi: 10.1080/00401706.1991.10484773
   Web of Science ®Google Scholar
• Laurent RTS, Cook RD. Leverage, local influence and curvature in nonlinear regression. Biometrika. 1993;80(1):99–106. doi: 10.1093/biomet/80.1.99
   Web of Science ®Google Scholar
• Lemonte AJ, Patriota AG. Influence diagnostics in Birnbaum-Saunders nonlinear regression models. J Appl Stat. 2011;38(5):871–884. doi: 10.1080/02664761003692357
   Web of Science ®Google Scholar
• Ramsey JB. Tests for specification errors in classical linear least-squares regression analysis. J R Stat Soc B. 1969;31(2):350–371.
   Google Scholar
• Ramsey JB, Gilbert R. A Monte Carlo study of some small sample properties of tests for specification error. J Am Stat Assoc. 1972;67(337):180–186. doi: 10.1080/01621459.1972.10481223
   Web of Science ®Google Scholar
• Davidson R, MacKinnon JG. Several tests for model specification in the presence of alternative hypotheses. Econometrica. 1981;49(3):781–793. doi: 10.2307/1911522
   Web of Science ®Google Scholar
• Hagemann A. A simple test for regression specification with non-nested alternatives. J Econom. 2012;166(2):247–254. doi: 10.1016/j.jeconom.2011.09.037
   Web of Science ®Google Scholar
• Bezanson J, Edelman A, Karpinski S, et al. Julia: a fresh approach to numerical computing. SIAM Rev. 2017;59(1):65–98. doi: 10.1137/141000671
   Web of Science ®Google Scholar
• R Core Team. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2018. Available from: https://www.R-project.org/.
   Google Scholar
• Lemonte AJ. Robust inference for Birnbaum-Saunders regressions. J Stat Comput Simul. 2016;86(3):611–622. doi: 10.1080/00949655.2015.1027203
   Web of Science ®Google Scholar
• Huet S, Bouvier A, Poursat MA. Statistical tools for nonlinear regression: a practical guide with S-PLUS and R examples. 2nd ed. New York: Springer; 2004.
   Google Scholar