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Bias and skewness in a general extreme-value regression model. (English) Zbl 1328.62407

Summary: In this paper we introduce a general extreme-value regression model and derive D. R. Cox and E. J. Snell’s [J. R. Stat. Soc., Ser. B 30, 248–265 (1968; Zbl 0164.48903)] 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 K. O. Bowman and L. R. Shenton’s formula [Commun. Stat., Simulation Comput. 17, No. 2, 343–348 (1988; Zbl 0695.62041)]. A simulation study with results obtained with the use of Cox and Snell’s [loc. cit.] formulae is discussed. Practical uses of this model and of the derived formulae for bias correction are also presented.

MSC:

62J05 Linear regression; mixed models
62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)

Software:

SPLIDA; Ox
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References:

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