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Compositional regression modeling under tilted normal errors: an application to a Brazilian Super League Volleyball data set. (English) Zbl 1449.62158
Summary: Simplistically, compositional data are characterized by components representing proportions or fractions of a whole. In this study, we aimed to apply a compositional regression model using Additive Log-Ratio (ALR) transformation for the response variables and assuming asymmetric errors, more specifically, the tilted normal distribution. This distribution is an alternative to the skew normal distribution. The inferential procedure is based on the usual maximum likelihood estimation. A simulation study was performed to verify the asymptotic properties of the maximum likelihood estimates. Real data set on percentages of players’ points in the Brazilian Super League 2014/2015 was used to illustrate the proposed methodology and also to compare our modeling with the skew normal and normal distributions.

MSC:
62J05 Linear regression; mixed models
62P99 Applications of statistics
Software:
Maxlik; sn; R; maxLik
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