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Mixed model-based additive models for sample extremes

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  • Padoan, S.A.
  • Wand, M.P.

Abstract

We consider additive models fitting and inference when the response variable is a sample extreme. Non-linear covariate effects are handled using the mixed model representation of penalised splines. A fitting algorithm based on likelihood approximations is derived. The efficacy of the resulting methodology is demonstrated via application to simulated and real data.

Suggested Citation

  • Padoan, S.A. & Wand, M.P., 2008. "Mixed model-based additive models for sample extremes," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2850-2858, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2850-2858
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    2. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    3. V. Chavez‐Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222, January.
    4. Francesco Pauli & Stuart Coles, 2001. "Penalized likelihood inference in extreme value analyses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 547-560.
    5. A. C. Davison & N. I. Ramesh, 2000. "Local likelihood smoothing of sample extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 191-208.
    6. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    8. Wand M. P., 2002. "Vector Differential Calculus in Statistics," The American Statistician, American Statistical Association, vol. 56, pages 55-62, February.
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    Cited by:

    1. M. de Carvalho & K. F. Turkman & A. Rua, 2013. "Dynamic threshold modelling and the US business cycle," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 535-550, August.
    2. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    3. Chiara Bocci & Enrica Caporali & Alessandra Petrucci, 2013. "Geoadditive modeling for extreme rainfall data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 181-193, April.

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