Cluster analysis of longitudinal profiles with subgroups. (English) Zbl 1393.62032
The authors propose a new approach to cluster longitudinal data based on nonparametric B-splines. The pairwise distance of the B-spline coefficients is used to group the longitudinal profiles, where the number of clusters is not specified in advance. The new method can be applied to unbalanced data sets, meaning that the longitudinal profiles of the subjects may consist of different numbers of points. The splines are fitted by a penalized regression and the pairwise distances of the spline coefficients is penalized to encourage subjects to fall into the same group. The authors establish the rate of convergence of these estimators and the recovery rate of the subgroups (depending on the distance between the groups). The results are illustrated in a simulation study and in a data example consisting of the weakly sales of different products over a total time of 11 years.
Reviewer: Martin Wendler (Greifswald)
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62G08 | Nonparametric regression and quantile regression |
| 62P20 | Applications of statistics to economics |
Keywords:
clustering; spline; penalized regression; longitudinal data; minimax concave penalty; model selection; nonparametric spline methodSoftware:
AS 136References:
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