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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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| Authors: | Irène Gijbels Rezaul Karim Anneleen Verhasselt |
| Institution: | 1. Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven, Celestijnenlaan 200B, Box 2400, Leuven (Heverlee), B-3001 Belgium;2. Department of Statistics, Jahangirnagar University, Dhaka, Bangladesh;3. Data Science Institute, Center for Statistics, Hasselt University, Agoralaan—Building D, Diepenbeek, B-3590 Belgium |
| 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. |
| Keywords: | Asymmetric density asymptotics maximum likelihood estimation method of moments quantiles |