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Response to the Letter to the Editor on ‘On Quantile‐based Asymmetric Family of Distributions: Properties and Inference’
Author(s) -
Gijbels Irène,
Karim Rezaul,
Verhasselt Anneleen
Publication year - 2020
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12424
Subject(s) - quantile , estimator , inference , mathematics , identification (biology) , statistical inference , econometrics , statistics , probabilistic logic , statistical model , maximum likelihood , computer science , artificial intelligence , botany , biology
Summary 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.