Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Robust extreme quantile estimation for Pareto-type tails through an exponential regression model

  • Richard Minkah (Department of Statistics and Actuarial Science, College of Basic and Applied Sciences, University of Ghana) ;
  • Tertius de Wet (Department of Statistics and Actuarial Science, Stellenbosch University) ;
  • Abhik Ghosh (Interdisciplinary Statistical Research Unit, Indian Statistical Institute) ;
  • Haitham M. Yousof (Department of Statistics, Mathematics and Insurance, Benha University)
  • Received : 2022.12.28
  • Accepted : 2023.08.01
  • Published : 2023.11.30
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Abstract

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

Keywords

Acknowledgement

Tertius de Wet's work was supported by the South African NRF under grant number 115038. Also, the research of Abhik Ghosh is partially supported by an INSPIRE Faculty Research Grant from the Department of Science and Technology, Government of India.

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