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Title: Registration method for functional data based on shape invariant model with $t$ distribution Authors:  Mariko Takagishi - Doshisha University (Japan) [presenting]
Hiroshi Yadohisa - Doshisha University (Japan)
Abstract: Registration for functional data aims at aligning each curves when the given data is misaligned, i.e. the beginning time point of the change is different depending on subjects. Shape Invariant Model (SIM) is a one of registration methods based on nonlinear regression models. Though the most existing SIM assume a normal distribution for the amplitude and phase variation, when there exist outliers, the estimation is often badly affected by them. Therefore, we propose SIM for $t-$distributions. The advantages of using $t-$distributions are; first, the effect of the outliers on the estimation is reduced since the $t-$distribution gives a bounded weight function. Second, since the model assuming normal distributions for amplitude and phase variation is nested with the one with assuming $t-$distributions, the update formula can be easily derived and the comparison with the existing normal model is simple.