## Multiscale clustering of nonparametric regression curves.(English)Zbl 1456.62078

Summary: In a wide range of modern applications, one observes a large number of time series rather than only a single one. It is often natural to suppose that there is some group structure in the observed time series. When each time series is modeled by a nonparametric regression equation, one may in particular assume that the observed time series can be partitioned into a small number of groups whose members share the same nonparametric regression function. We develop a bandwidth-free clustering method to estimate the unknown group structure from the data. More precisely speaking, we construct multiscale estimators of the unknown groups and their unknown number which are free of classical bandwidth or smoothing parameters. In the theoretical part of the paper, we analyze the statistical properties of our estimators. Our theoretical results are derived under general conditions which allow the data to be dependent both in time series direction and across different time series. The technical analysis of the paper is complemented by simulated and real-data examples.

### MSC:

 62G08 Nonparametric regression and quantile regression 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P20 Applications of statistics to economics

SiZer
Full Text:

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