Semi-parametric density estimation with TrioScale

• Autores: Paul H. C. Eilers, Mark de Rooij
• Localización: Proceedings of the 6th International Workshop on Compositional Data Analysis: Girona, 1-7 de juny de 2015 / coord. por Santiago Thió Fernández de Henestrosa, Josep Antoni Martín Fernández, 2015, ISBN 978-84-8458-451-3
• Idioma: inglés
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• Resumen

  • The TrioScale display transforms three-dimensional compositions to unbounded twodimensional coordinates. Then it is easy to estimate a smooth density for better visualization of scatterplots. We use penalized least squares smoothing of a detailed twodimensional histogram and back-transformation for display of a density in a ternary diagram. Originally we derived TrioScale by representing logarithms of proportions as negative squared distances from anchor points. An equivalent but simpler interpretation uses cyclic log-ratios, resulting in an unbounded triangular diagram with linear log-ratio axes. We also establish an equivalence to the isometric log-ratio transform. We apply our smoothing procedure to real-world data.