In this work, we introduce a regression model for double-bounded variables in the interval (0, 1) following a Kumaraswamy distribution. The model resembles a generalized linear model, in which the response’s median is modeled by a regression structure through the asymmetric Aranda-Ordaz parametric link function. We consider the maximum likelihood approach to estimate the regression and the link function parameters altogether. We study large sample properties of the proposed maximum likelihood approach, presenting closed-form expressions for the score vector as well as the observed and Fisher information matrices. We briefly present and discuss some diagnostic tools. We provide numeric evaluation of the finite sample inferences to show the performance of the estimators. Finally, to exemplify the usefulness of the methodology, we present and explore an empirical application.
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Lemma 3, in particular, is presented and proved in the supplementary material that accompanies the paper.
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Pumi, G., Rauber, C. & Bayer, F.M. Kumaraswamy regression model with Aranda-Ordaz link function. TEST 29, 1051–1071 (2020). https://doi.org/10.1007/s11749-020-00700-8
- Kumaraswamy distribution
- Aranda-Ordaz link function
- Regression model
- Asymptotic theory
Mathematics Subject Classification