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On a heavy-tailed parametric quantile regression model for limited range response variables

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Abstract

On the basis of a two-parameter heavy-tailed distribution, we introduce a novel parametric quantile regression model for limited range response variables, which can be very useful in modeling bounded response variables at different levels (quantiles) in the presence of atypical observations. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. We also propose a residual analysis to assess departures from model assumptions. Additionally, the local influence method is discussed, and the normal curvature for studying local influence on the maximum likelihood estimates is derived under a specific perturbation scheme. An application to real data is presented to show the usefulness of the new parametric quantile regression model in practice.

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Notes

  1. An outlying observation, or “outlier”, is one that appears to deviate markedly from other members of the sample in which it occurs.

  2. The voting data were obtained from http://www.onpe.gob.pe, whereas the HDI data were obtained from http://www.pnud.org.pe.

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Acknowledgements

The authors would like to express their deepest gratitude to the Associate Editor and the anonymous reviewers for their insightful comments and suggestions that greatly improved this paper. Artur Lemonte was supported by Grant 301808/2016–3 from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil). Germán Moreno-Arenas gratefully acknowledges the Mobility Program of the Universidad Industrial de Santander (UIS), Bucaramanga, Colombia.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil

    Artur J. Lemonte

  2. Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga, Colombia

    Germán Moreno-Arenas

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  1. Artur J. Lemonte
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  2. Germán Moreno-Arenas
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Correspondence to Artur J. Lemonte.

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Lemonte, A.J., Moreno-Arenas, G. On a heavy-tailed parametric quantile regression model for limited range response variables. Comput Stat 35, 379–398 (2020). https://doi.org/10.1007/s00180-019-00898-8

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