Self-Modelling Warping Functions
Tóm tắt
The paper introduces a semiparametric model for functional data. The warping functions are assumed to be linear combinations of q common components, which are estimated from the data (hence the name ‘self-modelling’). Even small values of q provide remarkable model flexibility, comparable with nonparametric methods. At the same time, this approach avoids overfitting because the common components are estimated combining data across individuals. As a convenient by-product, component scores are often interpretable and can be used for statistical inference (an example of classification based on scores is given).
Từ khóa
Tài liệu tham khảo
Gasser, 1991, The dynamics of linear growth in distance, velocity and acceleration, Ann. Hum. Biol., 18, 187, 10.1080/03014469100001522
Gasser, 1990, A method for determining the dynamics and intensity of average growth, Ann. Hum. Biol., 17, 459, 10.1080/03014469000001242
Hastie, 2001, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 10.1007/978-0-387-21606-5
Kneip, 1995, Model estimation in nonlinear regression under shape invariance, Ann. Statist., 23, 551, 10.1214/aos/1176324535
Kneip, 1992, Statistical tools to analyze data representing a sample of curves, Ann. Statist., 20, 1266, 10.1214/aos/1176348769
Ramsay, 2002, Applied Functional Data Analysis
Rønn, 2001, Nonparametric maximum likelihood estimation for shifted curves, J. R. Statist. Soc., 63, 243, 10.1111/1467-9868.00283
Wang, 1999, Synchronizing sample curves nonparametrically, Ann. Statist., 27, 439