A1216
Title: A robust coefficient of determination with the gamma divergence
Authors: Takeshi Kurosawa - Tokyo University of Science (Japan) [presenting]
Genta Nakane - Tokyo University of Science (Japan)
Abstract: In linear regressions, many robustification methods have been developed. The M estimation with a phi function is a very effective way to get robustification. A phi function with the redescending property gets robustification against large outliers. The Turkey weight is a very useful function with the redescending property. In linear regressions, an interest in a coefficient parameter estimation problem of explanatory variables is present. In addition to the coefficient parameter estimation, an evaluation of the obtained model is important in the linear models. The coefficient of determination is usually used for the evaluation. There are, however, few studies relating to the robustification of the coefficient of determination. It is insufficient to use the coefficient of determination using the estimate of the coefficient parameter with robustification. The coefficient of determination itself must be introduced with robustification. A few studies exist based on the typical robustification method. However, some methods do not behave well for a large outlier because they have a bias toward the true value of the coefficient of determination. Therefore, a new method is proposed to get robustification using a gamma divergence.
