A local moment type estimator for an extreme quantile in regression with random covariates

ABSTRACT

A conditional extreme quantile estimator is proposed in the presence of random covariates. It is based on an adaptation of the moment estimator introduced by Dekkers et al. (1989) in the classical univariate setting, and thus it is valid in the domain of attraction of the extreme value distribution, i.e., whatever the sign of the extreme value index is. Asymptotic normality of the estimator is established under suitable assumptions, and its finite sample behavior is evaluated with a small simulation study, where a comparison with an alternative estimator already proposed in the literature is provided. An illustration to a real dataset concerning the world catalogue of earthquake magnitudes is also proposed.

Keywords:

• Extreme quantile
• Local estimation
• Max-domain of attraction.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G32
• Secondary 62G05
• 62G30

Acknowledgments

The authors are grateful to two anonymous referees for their helpful and constructive comments on the preliminary version of the article.

Funding

This work was supported by a research grant (VKR023480) from VILLUM FONDEN and an international project for scientific cooperation (PICS-6416).