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A note on the asymptotic behavior of conditional extremes

Author

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  • Gangopadhyay, Ashis K.

Abstract

Suppose (X1, Z1),...,(Xn, Zn) are i.i.d. as (X, Z). Let Mnk be the maximum of all Zi's for which Xt is among the k-nearest neighbors of x0. It is shown that Mnk has the same asymptotic distribution as the maximum of k i.i.d. copies of the random variable Z given X = x0. Hence the asymptotic results related to the extremes of i.i.d. observations are applicable to this situation as well.

Suggested Citation

  • Gangopadhyay, Ashis K., 1995. "A note on the asymptotic behavior of conditional extremes," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 163-170, November.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:2:p:163-170
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    Cited by:

    1. Gardes, Laurent & Girard, Stéphane & Lekina, Alexandre, 2010. "Functional nonparametric estimation of conditional extreme quantiles," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 419-433, February.
    2. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    3. Gardes, Laurent & Girard, Stéphane, 2008. "A moving window approach for nonparametric estimation of the conditional tail index," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2368-2388, November.

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