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Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’

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  • Irène Gijbels
  • Rezaul Karim
  • Anneleen Verhasselt

Abstract

Rubio (2020) points out an identification problem for the four‐parameter family of two‐piece asymmetric densities introduced by Nassiri & Loris (2013). This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four‐parameter family however still makes sense. For the three‐parameter family, there is no identification problem. The main contribution in Gijbels et al. (2019a) is to provide asymptotic results for maximum likelihood and method‐of‐moments estimators for all members of the three‐parameter quantile‐based asymmetric family of distributions.

Suggested Citation

  • Irène Gijbels & Rezaul Karim & Anneleen Verhasselt, 2020. "Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’," International Statistical Review, International Statistical Institute, vol. 88(3), pages 797-801, December.
    • Handle: RePEc:bla:istatr:v:88:y:2020:i:3:p:797-801
    DOI: 10.1111/insr.12424
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    References listed on IDEAS

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    1. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    2. Frank Critchley & M. C. Jones, 2008. "Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 415-437, September.
    3. Vahid Nassiri & Ignace Loris, 2013. "A generalized quantile regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 1090-1105.
    4. Irène Gijbels & Rezaul Karim & Anneleen Verhasselt, 2019. "On Quantile‐based Asymmetric Family of Distributions: Properties and Inference," International Statistical Review, International Statistical Institute, vol. 87(3), pages 471-504, December.
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