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Bias and skewness in a general extreme-value regression model

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  • Barreto-Souza, Wagner
  • Vasconcellos, Klaus L.P.

Abstract

In this paper we introduce a general extreme-value regression model and derive Cox and Snell's (1968) general formulae for second-order biases of maximum likelihood estimates (MLEs) of the parameters. We obtain formulae which can be computed by means of weighted linear regressions. Furthermore, we give the skewness of order n-1/2 of the maximum likelihood estimators of the parameters by using Bowman and Shenton's (1988) formula. A simulation study with results obtained with the use of Cox and Snell's (1968) formulae is discussed. Practical uses of this model and of the derived formulae for bias correction are also presented.

Suggested Citation

  • Barreto-Souza, Wagner & Vasconcellos, Klaus L.P., 2011. "Bias and skewness in a general extreme-value regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1379-1393, March.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1379-1393
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    References listed on IDEAS

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    1. Cordeiro, Gauss M. & Botter, Denise A., 2001. "Second-order biases of maximum likelihood estimates in overdispersed generalized linear models," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 269-280, December.
    2. Chan, P.S. & Ng, H.K.T. & Balakrishnan, N. & Zhou, Q., 2008. "Point and interval estimation for extreme-value regression model under Type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4040-4058, April.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    5. Cordeiro, Gauss M. & Vasconcellos, Klaus L. P., 1997. "Bias correction for a class of multivariate nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 155-164, September.
    6. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
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