Coefficients of determination for least absolute deviation analysis |
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| Affiliation: | 1. Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran;2. Department of Gas Engineering, Ahwaz Faculty of Petroleum, Petroleum University of Technology, Ahwaz, Iran;3. Institute of Process Engineering and Environmental Technology, Dresden University of Technology, Dresden, Germany;1. IDMEC, Instituto Superior Técnico, Universidade de Lisboa,Av. Rovisco Pais, 1049-001, Lisboa, Portugal;2. ISEL, GI-MOSM, Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007,Lisboa, Portugal;1. ICTEAM Institute, UCLouvain, Belgium;2. Florida State University, USA |
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| Abstract: | The least-absolute deviation or l1 analysis of a linear model is an important alternative to the classical least squares analysis from the point of view of efficiency for longer-tailed error distributions and robustness to the presence of outliers. In this paper two coefficients of determination are proposed for the least-absolute deviation analysis. It is shown that they have desirable properties as measures of multiple association. Both fixed and random predictor variable cases are considered. In the case of random predictor variables, the sample coefficients of determination are shown to be consistent estimators of appropriate population parameters. |
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